can anyone help me with this
Find the general solution of x.dy/dx-y=x^2.e^x
thanks for any help
Put in standard form
$\displaystyle (1)\;\;\;\frac{dy}{dx} - \frac{y}{x} = x e^x$
The integrating factor is $\displaystyle \mu = exp(\int -\frac{1}{x}\,dx) = \frac{1}{x}$. Multiplying (1) by this gives
$\displaystyle \frac{1}{x} \left( \frac{dy}{dx} - \frac{y}{x} \right) = \frac{d}{dx} \left( \frac{1}{x} \cdot y \right) = e^x$
If you let $\displaystyle u = \frac{y}{x}$ your equation will separate.