Solving a differential equation given a general solution The general solution to
$y'''+(a+1)y''+(a+5)y'+5y=0$
(where $a$ is a real-valued constant) is
$y=c_1e^{-2t}\sin t+c_2y_2+c_3y_3$
Find $a$, $y_2$, and $y_3$.
I thought that finding the characteristic equation would help.  So I started as:
$r^3+(a+1)r^2+(a+5)r+5=0$
But it doesn't seem to really help with anything, so I'm not quite sure where to go from here.  Can I make some assumptions based on the general solution?
Thanks!

You could just plug $e^{-2t}\sin t$ into the differential equation to get $a$. 
