List of top Mathematics Questions on Differential Equations asked in CBSE CLASS XII

Find the particular solution of the differential equation \( \frac{dy}{dx} - 3y \cot x = \sin 2x \), given that \( y = 2 \) when \( x = \frac{\pi}{2} \).

Assertion (A) : One of the particular solutions of the differential equation \( \frac{dy}{dx} = e^{x+y} \) can be \( e^x + e^{-y} = -2 \).
Reason (R) : \( e^x + e^{-y} = C \) is the general solution of the differential equation \( \frac{dy}{dx} = e^{x+y} \).

Find the general solution of the differential equation: \( y \log_e y \frac{dx}{dy} + x = \frac{y^2}{2} \).

Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

Solve the differential equation \[ x\frac{dy}{dx}=y-x\sin^2\left(\frac{y}{x}\right), \quad \text{given that } y(1)=\frac{\pi}{6}. \]

The integrating factor of the differential equation $2x\frac{dy}{dx}-y=3$ is

The general solution of the differential equation $xdy-ydx=0$ is