List of top Mathematics Questions on Integrating Factor asked in CUET (UG)

General solution of the differential equation \[ \frac{dy}{dx}=e^{x-y}+3x^{2}e^{-y} \] is:
For the linear differential equation \[ \frac{dy}{dx} + \frac{2}{x}y = x^2 \] calculate the integrating factor (I.F.).
Find the integrating factor (I.F.) for the linear differential equation: \[ \frac{dy}{dx} - y\tan x = e^x \]
Find the integrating factor (I.F.) for the linear differential equation: \[ \frac{dy}{dx} + \frac{2x}{1+x^2}y = \frac{1}{(1+x^2)^2} \]
Solve: \[ \frac{dy}{dx} + y = e^x, \qquad y(0)=2 \]
Match List-I with List-II:
Integrating factor of xdy − (y + 2x2)dx = 0