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**1. Homework Statement**

Solve y"+4y'=sin 3t subject to y(0)=y'(0)=0 using Laplace Transform

**3. The Attempt at a Solution**

So I got:

[tex]s^2Y(s)-sy(0)-y'(0)+4[sY(s)-y(0)]=\frac{3}{s^2+9}[/tex]

[tex]\Rightarrow Y(s)=\frac{3}{(s^2+9)(s^2+4)}[/tex]

Now it looks like two irreducible quadratics, which I know should not be too bad, but I have never dealt with more than one.

Now am I correct to say that

[tex]\frac{3}{(s^2+9)(s^2+4)}=\frac{Ax+B}{s^2+9}+\frac{Cx+D}{s^2+4}[/tex]

This is where I think I have the problem... the notation.

Thanks!