# 2nd degree differential equation with non-constant coefficients

I'm having a really hard time solving

$$xy'' + 2y' + 4xy = 0$$

I basically tried a lot of substitutions and series but couldn't find it. I realize this isn't as hard as I make it out to be so I'm assuming there is a certain trick that I am not seeing.

Have you seen $y''+p(x)y'+q(x)y=0$ before? – Jack Dec 11 '11 at 13:29
Let be $z = xy$. We have $z''= 2y' + xy''$ e the equation becomes $$z'' + 4 z = 0$$