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y"+2y'+y=12.5e

^{-t}

I'm not sure on which method to use. Here's my attempt using the undetermined coefficients method:

→y"+2y'+y=12.5e

^{-t}

r

^{2}+2r+1=0

r=-1 *not even sure if this part is useful

→y

_{p}=e

^{-t}

y

_{p}'=-e

^{-t}

y

_{p}"=e

^{-t}

→y"+2y'+y=12.5e

^{-t}

(e

^{-t})+2(-e

^{-t})+(e

^{-t})=12.5e

^{-t}

e

^{-t}(1-2+1)=e

^{-t}(12.5)

This is where I get stuck; I don't believe I'm taking the right approach from the get-go. Any help would be greatly appreciated.