Question

Need help with an Inverse Laplace Transform

Answer 1

\[\frac{ s^2+20s+20 }{s^3+4s^2+7s+30}\]

The bottom simplifies into \[(s+6)(s^2-2s+5)\]

Which turns into
\[\frac{ A }{ s+6 }+\frac{ Bs+C }{s^2-2s+5}\]

Then I'm stuck

Answer 2

@cwrw238 , @zepdrix , @wio

Answer 3

Well you've broken the fraction up. Now you need to equate to solve for the coefficients.

\[s^{2}+20s+20=A(s^{2}-2s+5)+(Bs+C)(s+6)\]
\[s^{2}+20s+20=As^{2}-2As+5A+Bs^{2}+6Bs+Cs+6C\]
\[s^{2}+20s+20=(A+B)s^{2}+(-2A+6B+C)s+(5A+6C)\]
Match up the powers on each side to find:
\[A+B=1\]\[-2A+6B+C=20\]\[5A+6C=20\]

You can solve the system of equations to get the constants.