Solve differential equation $y'' = -a y +\frac by$ I am trying to solve for y(t):
$$y'' =-ay + \frac by$$
I have tried a lot, but haven't succeeded so far. Actually I am not sure there is a 'nice' solution. Do any of you have ideas of how to solve this?

Try substituting $y'=p(y)$
Then $y''=\frac{d}{dx}(y')=p'_x=p'_yy'=p'p$
Then your equation is $p'p=-ay+\frac{b}{y}$, where $y$ is considered independent.
