Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

(xy² +x)dx + (y–x²y)dy=0

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

where

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

(y")² +(y')²+ sin y =0

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

Form the differential equation of the family of curves represented by y² = (x – c)³.

Form the differential equation corresponding to y = e^mx by eliminating m.

Form the differential equation from the following primitives where constants are arbitrary:

y² = 4ax

Form the differential equation from the following primitives where constants are arbitrary:

y = cx + 2c² + c³

Form the differential equation from the following primitives where constants are arbitrary:

xy = a²

Form the differential equation from the following primitives where constants are arbitrary:

y = ax² + bx + c

Form the differential equation of the family of curves y = Ae^2x + Be^–2x, where A and B are arbitrary constants.

Form the differential equation of the family of curves,

x = A cos nt + B sin nt, where A and B are arbitrary constant.

Form the differential equation corresponding to y² = a(b – x²) by eliminating a and b.

Form the differential equation corresponding to y² – 2 ay + x² = a² by eliminating a.

Form the differential equation corresponding to (x – a)² + (y – b)² = r² by eliminating a and b.

Form the differential equation of all the circles which pass through the origin and whose centers lie on the y – axis.

Find the differential equation of all the circles which pass through the origin and whose centers lie on the x - axis.

Assume that a raindrop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the raindrop.

Find the differential equation of all the parabolas with latus rectum ‘4a' and whose axes are parallel to the x - axis.

Form the differential equation having y = (sin^–1 x)² + A cos^–1 x + B, where A and B are arbitrary constants, as its general solution.

Form the differential equation of the family of curves represented by the equation (a being the parameter):

i. (2x + a)² + y² = a²

ii. (2x – a)² – y² = a²

iii. (x – a)² + 2y² = a²

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

x² + y² = a²

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

x² – y² = a²

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

y² = 4ax

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

x² + (y – b)² = 1

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

(x – a)² – y² = 1

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

y² = 4 a (x – b)

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

y = ax³

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

x² + y² = ax³

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

y = e^ax

Form the differential equation representing the family of ellipses having the center at the origin and foci on the x - axis.

Form the differential equation of the family of hyperbolas having foci on x - axis and center at the origin.

Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.

Verify that y = 4 sin 3x is a solution of the differential equation

Show that y = ae^2x + be^–x is a solution of the differential equation

Show that the function y = A cos x + B sin x is a solution of the differential equation

Show that the function y = A cos2x – B sin 2x is a solution of the differential equation

Show that y = Ae^Bx is a solution of the differential equation

Verify that is a solution of the differential equation

Verify that y² = 4ax is a solution of the differential equation

Show that Ax² + By² =1 is a solution of the differential equation

Show that y = ax³ + bx² + c is a solution of the differential equation

Show that is a solution of the differential equation= 0.

Show that y = e^x (A cosx + B sinx) is a solution of the differential equation

Verify that y = cx + 2c² is a solution of the differential equation

Verify that y = –x – 1 is a solution of the differential equation (y – x)dy – (y² – x²)dx = 0.

Verify that y² = 4a(x + a) is a solution of the differential equation

Verify that is a solution of the differential equation

Verify that is a solution of the differential equation.

Verify that is a solution of the differential equation

Show that the differential equation of which is a solution is

Show that y = e^–x + ax + b is solution of the differential equation

For each of the following differential equations verify that the accompanying function is a solution.

Differential equation

i.

ii.

iii.

iv.

v.

Function

For each of the following initial value problems verify that the accompanying function is a solution:

Function: y = log x

For each of the following initial value problems verify that the accompanying function is a solution:

For each of the following initial value problems verify that the accompanying function is a solution:

Function: y=sin x

For each of the following initial value problems verify that the accompanying function is a solution:

Function: y=e^x+1

For each of the following initial value problems verify that the accompanying function is a solution:

Function: y = e^-x+2

For each of the following initial value problems verify that the accompanying function is a solution:

Function: y = sin x + cos x

For each of the following initial value problems verify that the accompanying function is a solution:

Function: y = e^x + e^-x

For each of the following initial value problems verify that the accompanying function is a solution:

Function: y = e^x+e^2x

For each of the following initial value problems verify that the accompanying function is a solution:

Function: y=xe^x + e^x

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

(sinx + cosx)dy + (cosx – sinx) dx = 0

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following differential equations

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

(1 + x²)dy = (xy)dx

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equation:

Solve the following differential equation:

dy + (x + 1)(y + 1) dx = 0

Solve the following differential equation:

Solve the following differential equation:

Solve the following differential equation:

Solve the following differential equation:

Solve the following differential equation:

Solve the following differential equation:

Solve the following differential equation:

Solve the following differential equation:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

Solve the following initial value problem:

when

Solve the following initial value problem:

Solve the differential equation given that when

Solve the differential equation given that when

Solve the differential equation given that when

Find the particular solution of given that when

Find the solution of the differential equation given that when

Find the particular solution of the differential equation given that when

Find the equation of a curve passing through the point (0, 0) and whose differential equation is

For the differential equation Find the solution curve passing through the point (1, -1).

The volume of a spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of the balloon after t seconds.

In a bank principal increases at the rate of r% per year. Find the value of r if ` 100 double itself in 10 years (log_e 2 = 0.6931).

In a bank principal increases at the rate of 5% per year. An amount of ` 1000 is deposited with this bank, how much will it worth after 10 years (e^0.5 = 1.648).

In a culture the bacteria count is 100000. The number is increased by 10% in 2 hours. In how many hours will the count reach 200000, if the rate of growth of bacteria is proportional to the number present.

If y(x) is a solution of the differential equation and y(0) = 1, then find the value of y(π/2).

Find the particular solution of the differential equation given that y = 0 when
x = 1.

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

(x + y)(dx–dy) = dx + dy

Solve the following differential equations:

Solve the following differential equations:

Solve the following equations:

x²dy + y(x + y)dx = 0

Solve the following equations:

Solve the following equations:

Solve the following equations:

Solve the following equations:

(x² – y²)dx – 2xydy = 0

Solve the following equations:

Solve the following equations:

Solve the following equations:

Solve the following equations:

Solve the following equations:

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

.

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

x

Solve the following differential equations :

Solve the following differential equations :

(x² + 3xy + y²)dx – x²dy=0

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve each of the following initial value problems

(x² + y²)d x = 2xy dy, y(1) = 0

Solve each of the following initial value problems

,y(e) = 0

Solve each of the following initial value problems

,y(1) = 0

Solve each of the following initial value problems

(xy–y²)dx+x²dy=0,y(1) = 1

Solve each of the following initial value problems

,y(1) = 2

Solve each of the following initial value problems

Solve each of the following initial value problems

,y(1) = 1

Solve each of the following initial value problems

Solve each of the following initial value problems

,y(2) = x

Find the particular solution of the differential equation given that when x = 1, y = π/4

Find the particular solution of the differential equation given that when x = 1, y = 0

Find the particular solution of the differential equation given that when y = 1, x = 0

Show that the family of curves for which is given by

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

Solve the following differential equations :

xdy = (2y + 2x⁴ + x²)dx

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

(x + tan y)dy = sin 2y dx

Solve the following differential equations:

dx + xdy = e^–ysec²ydy

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the following differential equations:

Solve the differential equation given that when x = 2, y = 1.

Find one-parameter families of solution curves of the following differential equations:

, m is a given real number

Find one-parameter families of solution curves of the following differential equations:

Find one-parameter families of solution curves of the following differential equations:

Find one-parameter families of solution curves of the following differential equations:

Find one-parameter families of solution curves of the following differential equations:

Find one-parameter families of solution curves of the following differential equations:

Find one-parameter families of solution curves of the following differential equations:

Find one-parameter families of solution curves of the following differential equations:

Find one-parameter families of solution curves of the following differential equations:

Find one-parameter families of solution curves of the following differential equations:

e^–ysec²ydy = dx + xdy

Find one-parameter families of solution curves of the following differential equations:

Find one-parameter families of solution curves of the following differential equations:

Solve each of the following initial value problems:

y’ + y = e^x,

Solve each of the following initial value problems:

, y(1) = 0

Solve each of the following initial value problems:

, y(0) = 0

Solve each of the following initial value problems:

, y(1) = 0

Solve each of the following initial value problems:

, y(0) = 0

Solve each of the following initial value problems:

, y(0) = 1

Solve each of the following initial value problems:

, y(0) = 1

Solve each of the following initial value problems:

,

Solve each of the following initial value problems:

,

Solve each of the following initial value problems:

,

Solve each of the following initial value problems:

, y = 0 when

Solve each of the following initial value problems:

, y = 2 when

Solve each of the following initial value problems:

,

Solve each of the following initial value problems:

dy = cos x (2 – y cosec x)dx

Solve each of the following initial value problems:

, tan x ≠ 0 given that y = 0 when

Find the general solution of the differential equation.

Find the general solution of the differential equation

Solve the differential equation

Find the particular solution of the differential equation y ≠ 0 given that x = 0 when

Solve the following differential equation

The surface area of a balloon being inflated, changes at a rate proportional to time t. If initially its radius is 1 unit and after 3 seconds it is 2 units, find the radius after time t.

A population grows at the rate of 5% per year. How long does it take for the population to double?

The rate of growth of a population is proportional to the number present. If the population of a city doubled in the past 25 years, and the present population is 100000, when will the city have a population of 500000?

[Given log_e 5 = 1.609, log_e 2 = 0.6931]

In a culture, the bacteria count is 100000. The number is increased by 10% in 2 hours. In how many hours will the count reach 20000, if the rate of growth of bacteria is proportional to the number present?

If the interest is compounded continuously at 6% per annum, how much worth ₹ 1000 will be after ten years? How long will it take to double ₹ 1000?

[Given e^0.6 = 1.822]

The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given the number triples in 5 hrs, find how many bacteria will be present after 10 hours. Also find the time necessary for the number of bacteria to be 10 times the number of initial present.

[Given log_e 3 = 1.0986, e^2.1972 = 9]

The population of a city increases at a rate proportional to the number of inhabitants present at any time t. If the population of the city was 200000 in 1990 and 25000 in 2000, what will be the population in 2010?

A ban pays interest by continuous compounding, that is, by treating the interest rate as the instantaneous rate of change of principal. Suppose in an account interest accrues at 8% per year, compounded continuously. Calculate the percentage increase in such an account over one year.

[Take e^0.08≈1.0833]

In a simple circuit of resistance R, self inductance L and voltage E, the current i at any time t is given by If E is constant and initially no current passes through the circuit, prove that

The decay rate of radium at any time t is proportional to its mass at that time. Find the time when the mass will be halved of its initial mass.

Experiments show that radium disintegrates at a rate proportional to the amount of radium present at the moment. Its half – life is 1590 years. What percentage will disappear in one year?

The slope of the tangent at a point P(x, y) on a curve is If the curve passes through the point (3, – 4), find the equation of the curve.

Find the equation of the curve which passes through the point (2, 2) and satisfies the differential equation

Find the equation of the curve passing through the point and tangent at any point of which makes an angle with the x – axis.

Find the curve for which the intercept cut – off by a tangent on the x – axis is equal to four times the ordinate of the point of contact.

Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y + 2(x + 1) = 2e^2x.

The tangent at any point (x, y) of a curve makes an angle with the x - axis. Find the equation of the curve if it passes through (1, 2).

Find the equation of the curve such that the portion of the x - axis cut off between the origin and the tangent at a point is twice the abscissa and which passes through the point (1, 2).

Find the equation to the curve satisfying and passing through (1, 0).

Find the equation of the curve which passes through the point (3, – 4) and has the slope at any point (x, y) on it.

Find the equation of the curve which passes through the origin and has the slope x + 3y – 1 at any point (x, y) on it.

At every point on a curve, the slope is the sum of the abscissa and the product of the ordinate and the abscissa, and the curve passes through (0, 1). Find the equation of the curve.

A curve is such that the length of the perpendicular from the origin on the tangent at any point P of the curve is equal to the abscissa of P. Prove that the differential equation of the curve is and hence find the curve.

Find the equation of the curve which passes through the point (1, 2) and the distance between the foot of the ordinate of the point of contact and the point of intersection of the tangent with the x - axis is twice the abscissa of the point of contact.

The normal to a given curve at each point (x, y) on the curve passes through the point (3, 0). If the curve contains the point (3, 4), find its equation.

The rate of increase of bacteria in a culture is proportional to the number of bacteria present, and it is found that the number doubles in 6 hours. Prove that the bacteria becomes eight times at the end of 18 hours.

Radium decomposes at a rate proportional to the quantity of radium present. It is found that in 25 years, approximately 1.1% of a certain quantity of radium has decomposed. Determine approximately how long it will take for one - half of the original amount of radium to decompose?

[Given log_e0.989 = 0.01106 and log_e2 = 0.6931]

Show that all curves for which the slope at any point (x, y) on it is are rectangular hyperbola.

The slope of the tangent at each point of a curve is equal to the sum of the coordinates of the point. Find the curve that passes through the origin.

Find the equation of the curve passing through the point (0, 1) if the slope of the tangent to the curve at each of its point is equal to the sum of the abscissa and the product of the abscissa and the ordinate of the point.

The slope of a curve at each of its points is equal to the square of the abscissa of the point. Find the particular curve through the point ( – 1, 1).

Find the equation of the curve that passes through the point (0, a) and is such that at any point (x, y) on it, the product of its slope and the ordinate is equal to the ab.

The x - intercept of the tangent line to a curve is equal to the ordinate of the point of contact. Find the particular curve through the point (1, 1).

Define a differential equation.

Define a differential equation.

Define order of a differential equation

Define order of a differential equation

Define degree of a differential equation

Define degree of a differential equation

Write the differential equation representing the family of straight lines y = Cx + 5, where C is an arbitrary constant.

Write the differential equation representing the family of straight lines y = Cx + 5, where C is an arbitrary constant.

Write the differential equation obtained by eliminating the arbitrary constant C in the equation x² – y² = C².

Write the differential equation obtained by eliminating the arbitrary constant C in the equation x² – y² = C².

Write the differential equation obtained eliminating the arbitrary constant C in the equation xy = C².

Write the differential equation obtained eliminating the arbitrary constant C in the equation xy = C².

Write the order of the differential equation

Write the order of the differential equation

Write the order and degree of the differential equation

Write the order and degree of the differential equation

Write the degree of the differential equation

Write the degree of the differential equation

Write the order of the differential equation of the family of circles touching X-axis at the origin.

Write the order of the differential equation of the family of circles touching X-axis at the origin.

Write the order of the differential equation of all non-horizontal lines in a plane.

Write the order of the differential equation of all non-horizontal lines in a plane.

If sin x is an integrating factor of the differential equation dy/dx + Py = Q, then write the value of P.

If sin x is an integrating factor of the differential equation dy/dx + Py = Q, then write the value of P.

Write the order of the differential equation of the family of circles of radius r.

Write the order of the differential equation of the family of circles of radius r.

Write the order of the differential equation whose solution is y = a cos x + b sin x + c e^–x.

Write the order of the differential equation whose solution is y = a cos x + b sin x + c e^–x.

Write the order of the differential equation associated with the primitive y = C₁ + C₂ e^x + C₃ e^–2x + C₄, where C₁, C₂, C₃, C₄ are arbitrary constants.

Write the order of the differential equation associated with the primitive y = C₁ + C₂ e^x + C₃ e^–2x + C₄, where C₁, C₂, C₃, C₄ are arbitrary constants.

What is the degree of the following differential equation?

What is the degree of the following differential equation?

Write the degree of the differential equation

Write the degree of the differential equation

Write the degree of the differential equation

Write the degree of the differential equation

Write the differential equation representing family of curves y = mx, where m is arbitrary constant.

Write the differential equation representing family of curves y = mx, where m is arbitrary constant.

Write the degree of the differential equation

Write the degree of the differential equation

Write the degree of the differential equation

Write the degree of the differential equation

Write degree of the differential equation

Write degree of the differential equation

Write the degree of the differential equation

Write the degree of the differential equation

Write the order and degree of the differential equation

Write the order and degree of the differential equation

The degree of the differential equation

The degree of the differential equation

How many arbitrary constants are there in the general solution of the differential equation of order 3.

How many arbitrary constants are there in the general solution of the differential equation of order 3.

Write the order of the differential equation representing the family of curves y = ax + a³.

Write the order of the differential equation representing the family of curves y = ax + a³.

Find the sum of the order and degree of the differential equation

Find the sum of the order and degree of the differential equation

Find the solution of the differential equation

Find the solution of the differential equation

Mark the correct alternative in each of the following:

Mark the correct alternative in each of the following:

The general solution of the differential equation is:

Mark the correct alternative in each of the following:

Integrating factor of the differential equation is

Mark the correct alternative in each of the following:

The degree of the differential equation is

Mark the correct alternative in each of the following:

The degree of the differential equation is

Mark the correct alternative in each of the following:

The general solution of the differential equation is

Mark the correct alternative in each of the following:

The differential equation obtained on eliminating A and B from y = A cos ωt + B sin ωt, is

Mark the correct alternative in each of the following:

The equation of the curve whose slope is given by x > 0, y > 0 and which passes through the point (1, 1) is

Mark the correct alternative in each of the following:

The order of the differential equation whose general solution is given by

y = c₁cos (2x + c₂) – (c₃ + c₄) a^{x+ c5} + c₆ sin (x – c₇) is

Mark the correct alternative in each of the following:

The solution of the differential equation represents a circle when

Mark the correct alternative in each of the following:

The solution of the differential equation with y(1) = 1 is given by

Mark the correct alternative in each of the following:

The solution of the differential equation is given by

Mark the correct alternative in each of the following:

The order of the differential equation satisfying is

Mark the correct alternative in each of the following:

The solution of the differential equation y₁y₃ = y₂² is

Mark the correct alternative in each of the following:

The general solution of the differential equation where g(x) is a given function of x, is

Mark the correct alternative in each of the following:

The solution of the differential equation is

Mark the correct alternative in each of the following:

The differential equation of the ellipse is

Mark the correct alternative in each of the following:

Solution of the differential equation is

Mark the correct alternative in each of the following:

The equation of the curve satisfying the differential equation

y(x + y³)dx = x(y³ – x) dy and passing through the point (1, 1) is

Mark the correct alternative in each of the following:

The solution of the differential equation represents

Mark the correct alternative in each of the following:

The solution of the differential equation is

Mark the correct alternative in each of the following:

The differential equation satisfied by ax² + by² = 1 is

Mark the correct alternative in each of the following:

The differential equation which represents the family of curves y = e^Cx is

Mark the correct alternative in each of the following:

Which of the following transformations reduce the differential equation into the form

Mark the correct alternative in each of the following:

The solution of the differential equation is

Mark the correct alternative in each of the following:

If m and n are the order and degree of the differential equation then

Mark the correct alternative in each of the following:

The solution of the differential equation is

Mark the correct alternative in each of the following:

The solution of is

Mark the correct alternative in each of the following:

The family of curves in which the subtangent at any point of a curve is double the abscissae, is given by

Mark the correct alternative in each of the following:

The solution of the differential equation x dx + y dy = x²y dy – y² x dx, is

Mark the correct alternative in each of the following:

The solution of the differential equation is

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The differential equation has the general solution

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The solution of the differential equation is

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The solution of the differential equation is

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The differential equation n > 2 can be reduced to linear form by substituting

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If p and q are the order and degree of the differential equation then

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Which of the following is the integrating factor of ?

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What is integrating factor of ?

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Integrating factor of the differential equation is

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The degree of the differential equation is

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The order of the differential equation is

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The number of arbitrary constants in the general solution of differential equation of fourth order is

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The number of arbitrary constants in the particular solution of a differential equation of third order is

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Which of the following differential equations has y = C₁ e^x + C₂ e^–x as the general solution?

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Which of the following differential equations has y = x as one of its particular solution?

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The general solution of the differential equation is

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A homogeneous differential equation of the form can be solved by making the substitution.

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Which of the following is a homogeneous differential equation?

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The integrating factor of the differential equation

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The integrating factor of the differential equation is

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The general solution of the differential equation is

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The general solution of a differential equation of the type is

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The general solution of the differential equation e^x dy + (y e^x + 2x)dx = 0 is