Answer to Question #343124 in Differential Equations for Tobias Felix

Question

Find the Laplace transforms of the following function:

7. L{t^2 -3cos4t}

Answer 1

$${\cal L}\{f\}(s)=\int_0^{\infty}f(t)e^{-st}dt$$ $${\cal L}\{t^2-3\cos4t\}(s)\\ =\int_0^{\infty}t^2e^{-st}dt-3\int_0^{\infty}\cos4te^{-st}dt\\ =\frac{2}{s^3}-3*\frac{s}{16+s^2}\\ =\frac{2}{s^3}-\frac{3s}{16+s^2}$$