1. ## differential equation

can anyone help me with this
Find the general solution of x.dy/dx-y=x^2.e^x
thanks for any help

2. Originally Posted by hmmmm
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

$(1)\;\;\;\frac{dy}{dx} - \frac{y}{x} = x e^x$

The integrating factor is $\mu = exp(\int -\frac{1}{x}\,dx) = \frac{1}{x}$. Multiplying (1) by this gives

$\frac{1}{x} \left( \frac{dy}{dx} - \frac{y}{x} \right) = \frac{d}{dx} \left( \frac{1}{x} \cdot y \right) = e^x$

If you let $u = \frac{y}{x}$ your equation will separate.