Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

e^x tan y dx + (1 – e^x) sec² y dy = 0

Find the general solution of each of the following differential equations:

sec²x tan y dx + sec²y tan x dy = 0

Find the general solution of each of the following differential equations:

cos x(1 + cos y)dx – sin y(1 + sin x)dy = 0

For each of the following differential equations, find a particular solution satisfying the given condition :

.. where a ∈ R and y = 2 when x = 0.

For each of the following differential equations, find a particular solution satisfying the given condition :

it being given that y = 1 when x = 0.

For each of the following differential equations, find a particular solution satisfying the given condition :

x dy = (2x² + 1) dx (x ≠ 0), given that
y = 1 when x = 1.

For each of the following differential equations, find a particular solution satisfying the given condition :

it being given that y = 1 when x = 0.

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

x² (y + 1) dx + y² (x – 1) dy = 0

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

y log y dx – x dy = 0

Find the general solution of each of the following differential equations:

x(x² – x² y²) dy + y(y² + x²y²) dx = 0

Find the general solution of each of the following differential equations:

(1 – x²) dy + xy (1 – y) dx = 0

Find the general solution of each of the following differential equations:

(1 – x²)(1 – y) dx = xy (1 + y) dy

Find the general solution of each of the following differential equations:

(y + xy) dx + (x – xy²) dy = 0

Find the general solution of each of the following differential equations:

(x² – yx²) dy + (y² + xy²) dx = 0

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

cos x(1 + cos y)dx – sin y(1 + sin x)dy = 0

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

(e^y + 1) cos x dx + e^y sin x dy = 0

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

Find the general solution of each of the following differential equations:

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

Find the general solution of each of the following differential equations:

Find the particular solution of the differential equation x(1 + y²) dx
-y(1 + x²) dy = 0, given that y = 1 when x = 0.

Find the general solution of each of the following differential equations:

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

Find the general solution of each of the following differential equations:

Solve the differential equation (x² – yx²)
dy + (y² + x²y²) dx = 0, given that y = 1 when x = 1.

Find the general solution of each of the following differential equations:

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

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

Solve the differential equation given that y(0) = 1.

Solve the differential equation given that y(2) = 3.

Solve given that y = 0 when x = 2.

Solve given that y = 1 when x = 0.

Solve given that y = 1 when x = 0.

Solve given that y = 2 when x = 0.

Solve given that y = 2 when

Solve (1 + x²) sec2 y dy + 2x tan y dx = 0, given that when x = 1.

Find the equation of the curve passing through the point whose differential equation is sin x cos y dx + cos x sin y dy = 0.

Find the equation of a curve which passes through the origin and whose differential equation is

A curve passes through the point (0, -2) and at any point (x, y) of the curve, the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point. Find the equation of the curve.

A curve passes through the point (-1, 1) and at any point (x, y) of the curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (-4, -3). Find the equation of the curve.

In a bank, principal increases at the rate fo r% per annum. Find the value of r if ` 100 double itself in 10 years.

(Given log_e 2 = 0.6931)

In a bank, principal increases at the rate of 5% per annum. An amount of ` 1000 is deposited in the bank. How much will it worth after 10 years?

(Given e^0.5 = 1.648)

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 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?