# Partial Fractions Question

I am currently doing a Laplace past exam question and I can't quite figure out the partial fraction area of the question. It is as follows

$$Y(p) = \dfrac{A}{p^2} + \dfrac{B}{p} + \dfrac {C(p+2)}{(p+2)^2 +1} + \dfrac {D}{(p+2)^2 +1}$$

Now what I have done so far is -

$A((p+2)^2 +1) + Bp + C(p+2)p^2 + Dp^2 = 5 + 10p$

After inserting $p=0, p=-2, p=1, p=-1$, I get the following simultaneous equations

$-2B + 4D = -16$

$B+2C+D=5$

$-B+C+D=-7$

as $A=1$ . From there I get $B=6,C=0,D=-1$ but the answers state that it's $B= 6/5, C=-6/5, D=-17/5$

Where did I go wrong? Your help would be much appreciated.

• You need $B p ((p+2)^2+1)$, not just $Bp$. – Daniel Fischer Jan 12 '14 at 12:44