List of top Mathematics Questions on Solution of Differential Equations asked in UP Board XII

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

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 \[ \frac{dy}{dx} = \frac{2x}{y^2}. \]