Answer to Question #343124 in Differential Equations for Tobias Felix

Question #343124

Find the Laplace transforms of the following function:

7. L{t^2 -3cos4t}


1
Expert's answer
2022-05-23T16:08:22-0400
"{\\cal L}\\{f\\}(s)=\\int_0^{\\infty}f(t)e^{-st}dt""{\\cal L}\\{t^2-3\\cos4t\\}(s)\\\\\n=\\int_0^{\\infty}t^2e^{-st}dt-3\\int_0^{\\infty}\\cos4te^{-st}dt\\\\\n=\\frac{2}{s^3}-3*\\frac{s}{16+s^2}\\\\\n=\\frac{2}{s^3}-\\frac{3s}{16+s^2}"

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