Answer to Question #343121 in Differential Equations for Tobias Felix

Question #343121

Find the Laplace transforms of the following function:

4. L{e^5t}


1
Expert's answer
2022-05-24T13:10:55-0400

"L({e^{5t}}) = \\int\\limits_0^\\infty {{e^{ - st}}{e^{5t}}} dt = \\int\\limits_0^\\infty {{e^{\\left( {5 - s} \\right)t}}} dt = \\frac{1}{{5 - s}}\\mathop {\\lim }\\limits_{x \\to \\infty } \\left. {{e^{\\left( {5 - s} \\right)t}}} \\right|_0^x = \\frac{1}{{5 - s}}\\mathop {\\lim }\\limits_{x \\to \\infty } \\left( {{e^{\\left( {5 - s} \\right)x}} - {e^0}} \\right) = \\frac{1}{{5 - s}}\\left( {0 - 1} \\right) = \\frac{1}{{s - 5}}"

Answer: "\\frac{1}{{s - 5}}"


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