Question

Find the general solution of the given differential equation. x2y' + x(x + 2)y = ex

Answer 1

`x^2y'+x(x+2)y=e^x`

`x^2e^xy'+x(x+2)e^xy=e^(2x)`

`\bigg(x^2e^xy\bigg)'=e^(2x)`

`x^2e^xy=\frac{e^(2x)}2+C`

`y=(e^x)/(2x^2)+\frac C{x^2e^x}`