List of top Mathematics Questions on Solution of Differential Equations

Determine the exact expression for the Integrating Factor (I.F.) of the following first-order linear differential equation: \( \frac{dy}{dx} - y\tan x = e^x \)
Find the solution of the differential equation: \[ \frac{dy}{dx} = 3x^2 \]
Find the general solution of the separable differential equation: \[ \frac{dy}{dx} = e^{x-y} + x^2e^{-y} \]
Find the general solution of the differential equation: \( \frac{dy}{dx} + \frac{y}{x} = x^2 \)

Solve the differential equation \[ (x + y) \, dy + (x - y) \, dx = 0, \quad \text{if} \quad y = 1 \text{ when } x = 1. \] 

The general solution of the differential equation ydx + xdy = 0 is:
The general solution of differential equation \(\frac{dy}{dx} - xy = e^{\frac{x^2}{2}}\)
The number of solutions of the equation \(xydx— (x2-y2)dy=0\) with \( y(2)=3\) is :
The solution of the differential equation \(\frac{dy}{dx}=-\frac{x}{y}\) is:

Find the particular solution of the differential equation: \[ \frac{dy}{dx} + y \cot x = 4x \csc x \text{(} x \neq 0 \text{)}. \] Given that \( y = 0 \) \(\text{ when}\) \( x = \frac{\pi}{2} \).

Find the particular solution of the differential equation \[ \frac{dy}{dx} + y \cot x = 2x + x^2 \cot x, (x \neq 0) \] given that \( y = 0 \) if \( x = \frac{\pi}{2} \).
Find the general solution of \[ \frac{dy}{dx} = \frac{x - 1}{2 + y}. \]
Find the equation of the curve which is passing through the point \( (1, 1) \), and whose differential equation is \[ x \, dy = (2x^2 + 1) \, dx, (x \neq 0). \]
Find the equation of the curve passing through $(-2,3)$ on which the gradient of the tangent at any point $(x,y)$ is \[ \frac{dy}{dx} = \frac{2x}{y^2}. \]
The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is:
The solution of the differential equation\(\frac{dy}{dx}= \frac{6}{x^2}; y(1) = 3\) is:
Solution of a differential equation  \((1+ y2)dx=(\tan^{-1}y - x)dy\) is :
The solution of the differential equation
{x4+6x2+2(x+y)} dx-xdy=0
subject to the condition y(1)=0 is