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## Homework Statement

I must find the solution of a differential equation, but I'm stuck with a problem of algebra;

## Homework Equations

The problem is

[tex]

y''+2y'+2y = sin(at)

[/tex]

With y(0) = y(0)' = 0

y''+2y'+2y = sin(at)

[tex]

s^2L[y]+2sL[y]+2L[y] = \frac{a}{s^2+a^2}

[/tex]

[tex]

L[y](s^2+2s+2) = \frac{a}{s^2+a^2}

[/tex]

[tex]

L[y] = \frac{a}{(s^2+2s+2)(s^2+a^2)}

[/tex]

## The Attempt at a Solution

I transform it;

[tex]

L[y] = \frac{a}{([s+1]^2+1)(s^2+a^2)}

[/tex]

[tex]

\frac{a}{([s+1]^2+1)(s^2+a^2)} = \frac{A(s+1)+B}{[s+1]^2+1}+\frac{C}{s^2+a^2}

[/tex]

[tex]

a = [A(s+1)+B](s^2+a^2) + C[(s+1)^2+1]

[/tex]

I just don't have a clue how to find A, B and C from here...

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