Synopsis:
Please check my work. I do not have a text "answers to odd problems" for reference as this is an "even" numbered problem. The following documents in good detail the steps taken to solve for this so that the root of any errors, if any occur, can easily be found. Your input is very graciously welcomed.
Given:
Find the inverse Laplace transform for the following by using partial fraction decomposition...
$$F(s)=\frac{4s+4}{s^2+16}$$
My Solution:
This is of the type having complex non-repeating factors...
$$F(s)=\frac{As+B}{(s-\alpha)^2+\beta^2}$$
Whose solution is...
$$f(t)=e^{\alpha t}\left[ A\cos(\beta t)+\frac{\alpha A+B}{\beta}\sin(\beta t) \right]$$
This yields...
$$f(t)=e^{0\cdot t}\left[ 4\cos(4\cdot t)+\frac{0\cdot4+4}{4}\sin(4\cdot t) \right]$$
$$=4\cdot\cos4t+\sin4t$$
Answer in Text:
No answer in text to compare this solution with.
Question:
I love solutions that are short, simple, and sweet as this but is it correct? Did you find any errors?