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## Homework Statement

Compute the general solution of y'' + 4y' + 20y =e

^{-2t}sin4t

## Homework Equations

## The Attempt at a Solution

after using determinants, I found the [tex]\lambda_1 = -2 + 4i[/tex] and [tex]\lambda_2 = -2 - 4i[/tex]

So the general solution would be y(t) = k

_{1}e

^{-2t}cos4t + k

_{2}e

^{-2t}sin4t + y

_{im}

to find y

_{im}, would I make it equal to Ae

^{-2t}e

^{4it}, find first and second derivative, and plug them in the original equation and then apply euler's method?