Answer to Question #343119 in Differential Equations for Tobias Felix

Question #343119

Find the Laplace transforms of the following function:

2. L{e^5t}


1
Expert's answer
2022-05-24T08:27:52-0400
"F(s)=L(e^{5t})=\\displaystyle\\int_{0}^{\\infin}e^{-st}e^{5t}dt"

"=\\lim\\limits_{A\\to\\infin}\\displaystyle\\int_{0}^{A}e^{-(s-5)t}dt=[-\\dfrac{e^{-(s-5)t}}{s-5}]\\begin{matrix}\n A \\\\\n 0\n\\end{matrix}"

"=-0+\\dfrac{1}{s-5}=\\dfrac{1}{s-5}"

"L(e^{5t})=\\dfrac{1}{s-5}"


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