Answer to Question #343132 in Differential Equations for Tobias Felix

Question #343132

Inverse Laplace Transforms

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


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


1
Expert's answer
2022-05-25T17:10:46-0400

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}"

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