Answer to Question #343131 in Differential Equations for Tobias Felix

Question #343131

Inverse Laplace Transforms

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


1. 1/(s+3)(s+7)


1
Expert's answer
2022-05-25T12:54:21-0400

1.


"\\dfrac{1}{(s+3)(s+7)}=\\dfrac{A}{s+3}+\\dfrac{B}{s+7}"

"=\\dfrac{As+7A+Bs+3B}{(s+3)(s+7)}"

"A+B=0"

"7A+3B=1"

"A=\\dfrac{1}{4}, B=-\\dfrac{1}{4}"


"L^{-1}(\\dfrac{1}{(s+3)(s+7)})=\\dfrac{1}{4}L^{-1}(\\dfrac{1}{s+3})"


"-\\dfrac{1}{4}L^{-1}(\\dfrac{1}{s+7})=\\dfrac{1}{4}e^{-3t}-\\dfrac{1}{4}e^{-7t}"


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