Answer to Question #343119 in Differential Equations for Tobias Felix

Question

Find the Laplace transforms of the following function:

2. L{e^5t}

Answer 1

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

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

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

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