Answer to Question #343132 in Differential Equations for Tobias Felix

Question

Inverse Laplace Transforms

Find L^-1 {F(s)} when F(s) is given by

1. s+5/(s+1)(s-3)

Answer 1

1.

$$\dfrac{s+5}{(s+1)(s-3)}=\dfrac{A}{s+1}+\dfrac{B}{s-3}$$

$$=\dfrac{As-3A+Bs+B}{(s+1)(s-3)}$$

$$A+B=1$$ $$-3A+B=5$$

$$A=-1, B=2$$

$$L^{-1}(\dfrac{s+5}{(s+1)(s-3)})=-L^{-1}(\dfrac{1}{s+1})$$

$$+2L^{-1}(\dfrac{1}{s-3})=-e^{-t}+2e^{3t}$$