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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!

3 Answers 3