Originally Posted by
Ackbeet I, for one, am not seeing why there has to be a
$\displaystyle \dfrac{B}{(s+2)^{2}}$
term when there isn't one in the LT. Is there one in the LT? If so, why didn't it cancel? Here's what I have from the original DE:
$\displaystyle y'' + 4y' + 4y = e^{-t}(\sin(t) + \cos(t)), y(0) = 0, y'(0) = 0.$
LT gives
$\displaystyle s^{2}Y+4sY+4Y=\dfrac{1}{(s+1)^{2}+1}+\dfrac{s+1}{( s+1)^{2}+1}=\dfrac{s+2}{(s+1)^{2}+1}.$ This implies
$\displaystyle Y(s+2)^{2}=\dfrac{s+2}{(s+1)^{2}+1},$ or
$\displaystyle Y(s+2)=\dfrac{1}{(s+1)^{2}+1},$ and hence
$\displaystyle Y=\dfrac{1}{(s+2)((s+1)^{2}+1)}.$
There's no $\displaystyle 1/(s+2)^{2}$ in there.
Did I do something wrong?