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mtxop2

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## Homework Statement

4y" + 4y' + 5y = 0

y(0) = 3

y'(0) = 1

## Homework Equations

yh = e^ax(c1cosbx + c2sinbx)

## The Attempt at a Solution

For the roots I got -1/2 + i and -1/2 - i so my a = -1/2 and b = 1

then I have to differentiate yh = e^(-1/2x)[c1cosx + c2sinx]

this is where I get this overly complicated equation and I was wondering if I could do integration by parts instead.

where I could get something like

yh = -1/2e^(-1/2x)[c1cosx + c2sinx] + [-c1sinx + c2cosx]e^(-1/2x)

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