Using Laplace, getting stuck on decomposition
I think I have a fair idea of how to solve my equations, using Laplace transform. But the partial fraction decomposition seems to elude me...
I get X and Y as such.
 = \frac{s^3+3s}{s^4+5s^2+4})
 = \frac{2}{s^4+5s^2+4})
I get this:
 = \frac{1}{s^2+1} - \frac{1}{s^2+4})
I pulled the handbrake here because wolfram alpha got something else...
Wolfram Alpha, see: Partition fraction expansion
If anyone could find it in their heart to ease me throw this one, so that I can solve my system of differential equations...
Re: Using Laplace, getting stuck on decomposition
Your answer can't be right because:
=\frac{1}{s^2+1}-\frac{1}{s^2+4}=\frac{(s^2+4)-(s^2+1)}{(s^2+1)(s^2+4)}=\frac{3}{(s^2+1)\cdot(s^2 +4)})
which is different from the original given )
.
We have =\frac{s^3+3s}{(s^2+1)(s^2+4)}=\frac{As+B}{s^2 +1}+\frac{Cs+D}{s^2+4})
If we proceed:
(s^2+4)+(Cs+D)(s^2+1)}{(s^2+1)(s^2+4)})
(s^ 2+4)})
s^3+(B+D)s^2+(4A+C)s+(4B+D)}{(s^2+1)(s ^2+4)})
This means: 
, 
, 
and 
Can you proceed?
Re: Using Laplace, getting stuck on decomposition
Thank you very much! I got it from here. I didn't write the proposed denominators correctly.
