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

Which of the following equations is NOT a Linear Differential Equation?

Solve the differential equation \( y e^y dx = (y^3 + 2x e^y) dy \), given that \( y(0) = 1 \).

Find the general solution of the differential equation \( (x^3 - 3xy^2) dx = (y^3 - 3x^2y) dy \).

Solve the differential equation $y \, dx + (x - y^3) \, dy = 0$.

If $y = P \cos(ux) + Q \sin(ux)$, where $P, Q,$ and $u$ are constants, show that $\frac{d^2y}{dx^2} + u^2y = 0$.

The general solution for the differential equation \( \frac{dy}{dx} = e^{3x - y} \) is :

The order and degree of differential equation \( \frac{d^2y}{dx^2} = 1 - \left( \frac{d^3y}{dx^3} \right)^2 \) is :

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