- #1
cdotter
- 305
- 0
Homework Statement
Find the inverse Laplace transform of [tex]\frac{2s+1}{s^2-2s+2}[/tex]
Homework Equations
The Attempt at a Solution
[tex]
\begin{align*}
L^{-1}\{ \frac{2s+1}{s^2-2s+2} \} &= 2 L^{-1}\{ \frac{s}{(s-1)^2+1} \} + L^{-1}\{ \frac{1}{(s-1)^2+1} \} \\
&= 2 L^{-1}\{ \frac{s}{(s-1)^2+1} \} + e^t sin(t) \\
&= L^{-1}\{ \frac{2s+1-1}{(s-1)^2+1} \} + e^t sin(t) \\
&= L^{-1}\{ \frac{2s-1}{(s-1)^2+1} \} + L^{-1}\{ \frac{1}{(s-1)^2+1} \} + e^t sin(t) \\
&= 2e^t cos(t) + e^t sin(t) + L^{-1}\{ \frac{1}{(s-1)^2+1} \} \\
&= 2e^t cos(t) + e^t sin(t) + e^t sin(t)
\end{align*}
[/tex]
My book has an answer of [itex]2e^t cos(t) + 3e^t sin(t)[/itex]. Am I making a mistake in the algebra?
Last edited: