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

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

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

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

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

Find a particular solution of the differential equation \( (x + 1) \frac{dy{dx} = 2 e^{-y} - 1 \), given that \( y = 0 \) when \( x = 0 \).}

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 \(\frac{dy}{dx} = e^{x+y}\).

The general solution of the differential equation: \( x^2 dy + y^2 dx = 0 \) is

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

Find the particular solution of the differential equation \( (1 + e^{2x})dy + (1 + y^2)e^x dx = 0 \), given that \( y(1) = 0 \).