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Write order and degree (if defined)of each of the following differential equations:
(3x + 5y)dy - 4x2 dx = 0
Verify that x2 = 2y2log y is a solution of the differential equation (x2 + y2) - xy = 0.
Verify that y = ex cos bx is a solution of the differential equation
Verify that y = is a solution of the differential equation (1 - x2)
Verify that y = (a + bx) e2x is the general solution of the differential equation
Verify that y = ex(A cos x + B sin x) is the general solution of the differential equation
Verify that y = A cos 2x - B sin 2x is the general solution of the differential equation = 0.
Verify that y = ae2x + be - x is the general solution of the differential equation
Show that y = ex(A cos x + B sin x) is the solution of the differential equation
Verify that y2 = 4a(x + a) is a solution of the differential equation
Verify that y = is a solution of the differential equation (1 + x2) + (2x - 1) = 0
Verify that y = is a solution of the differential equation
Verify that y = e - x + Ax + B is a solution of the differential equation
Verify that Ax2 + By2 = 1 is a solution of the differential equation
Verify that y = is a solution of the differential equation (1 + x2) + (1 + y2) = 0.
Verify that y = log (x + satisfies the differential equation.
Verify that y = e - 3x is a solution of the differential equation
Form the differential equation of the family of straight lines y=mx+c, where m and c are arbitrary constants.
Form the differential equation of the family of concentric circles x2+y2=a2, where a>0 and a is a parameter.
Form the differential equation of the family of curves, y=a sin (bx+c), Where a and c are parameters.
Form the differential equation of the family of curves x=A cos nt+ Bsin nt, where A and B are arbitrary constants.
Form the differential equation of the family of curves y=aebx, where a and b are arbitrary constants.
Form the differential equation of the family of curves y2=m(a2-x2), where a and m are parameters.
Form the differential equation of the family of curves given by (x-a)2+2y2=a2, where a is an arbitrary constant.
Form the differential equation of the family of curves given by x2+y2-2ay=a2, where a is an arbitrary constant.
Form the differential equation of the family of all circles touching the y-axis at the origin.
From the differential equation of the family of circles having centers on y-axis and radius 2 units.
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes
Form the differential equation of the family of circles having centers on the x-axis and radius unity.
Form the differential equation of the family of circles passing through the fixed point (a,0) and (-a,0), where a is the parameter.
Form the differential equation of the family of parabolas having a vertex at the origin and axis along positive y-axis.
Form the differential equation of the family of an ellipse having foci on the y-axis and centers at the origin.
Form the differential equation of the family of hyperbolas having foci on the x-axis and centers at the origin.