# Thread: second order differential eq

1. ## second order differential eq

x^2 y" - x y' + y = 2 log x+ x^2 log x + x^2 + 1/x

2. You can solve the homogeneous part via $y=x^m$.

3. You can also let $u = x y' - y$ so $u' = x y''$ so your equation becomes

$xu' - u = 2 \log x+ x^2 \log x + x^2 + 1/x$

a first order linear equation. Once you solve it you then solve $xy' - y = u$ which also a first order linear equation.

4. thank u!!