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(e5t)=0este5tdtF(s)=L(e^{5t})=\displaystyle\int_{0}^{\infin}e^{-st}e^{5t}dt

=limA0Ae(s5)tdt=[e(s5)ts5]A0=\lim\limits_{A\to\infin}\displaystyle\int_{0}^{A}e^{-(s-5)t}dt=[-\dfrac{e^{-(s-5)t}}{s-5}]\begin{matrix} A \\ 0 \end{matrix}

=0+1s5=1s5=-0+\dfrac{1}{s-5}=\dfrac{1}{s-5}

L(e5t)=1s5L(e^{5t})=\dfrac{1}{s-5}


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