Answer to Question #343134 in Differential Equations for Tobias Felix

Question #343134

Inverse Laplace Transforms

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


4. s+7/s^2+2s+5


1
Expert's answer
2022-05-26T17:15:06-0400

4.


"\\dfrac{s+7}{s^2+2s+5}=\\dfrac{s+1+6}{(s+1)^2+4}"




"=\\dfrac{s+1}{(s+1)^2+2^2}+6\\dfrac{1}{(s+1)^2+2^2}"




"L^{-1}(\\dfrac{s+7}{s^2+2s+5})=L^{-1}(\\dfrac{s+1}{(s+1)^2+2^2})"




"+6L^{-1}(\\dfrac{1}{(s+1)^2+2^2})=e^{-t}\\cos(2t)+\\dfrac{6}{2}e^{-t}\\sin (2t)"




"=e^{-t}\\cos(2t)+3e^{-t}\\sin (2t)"


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