Answer to Question #343123 in Differential Equations for Tobias Felix

Question #343123

Find the Laplace transforms of the following function:

6. L{2cos3t + 5sin3t}


1
Expert's answer
2022-05-24T13:54:05-0400
"{\\cal L}\\{f\\}(s)=\\int_0^{\\infty}f(t)e^{-st}dt""{\\cal L}\\{2\\cos3t+5\\sin3t\\}(s)\\\\\n=2\\int_0^{\\infty}\\cos3te^{-st}dt+5\\int_0^{\\infty}\\sin3te^{-st}dt\\\\\n=2*\\frac{s}{9+s^2}+5*\\frac{3}{9+s^2}\\\\\n=\\frac{2s}{9+s^2}+\\frac{15}{9+s^2}"

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