# Math Help - Second order non homogeneous differential equation

1. ## Second order non homogeneous differential equation

I have to solve this DE
((x+2)^2)y'' -2y=4

the hint says to get rid of the x+2 but I have no idea where to start from... do I have to replace x+2 with another variable or what?

2. I would replace the $x+2$ with $t=x+2,$ and you get

$\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=\dfrac {dy}{dx}.$ Hence, the DE becomes

$t^{2}\,\dfrac{d^{2}y}{dt^{2}}-2y=4.$

This equation is a Cauchy-Euler equation.