List of top Mathematics Questions on Integrating Factor

The integrating factor of the differential equation $(e^x - \sin y) dx + \cos y \, dy = 0$ is

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: