Answer to Question #217602 in Differential Equations for Fhumu

Question

L{2(t)H(t-3)}

Answer 1

$$L(H(t-3))=\dfrac{e^{-3s}}{s}$$

$$L(2H(t-3))=2\dfrac{e^{-3s}}{s}$$

$$L(2tH(t-3))=2(-1)^1\dfrac{d}{ds}(\dfrac{e^{-3s}}{s})$$

$$=-2\dfrac{-3se^{-3s}-e^{-3s}}{s^2}$$

$$=\dfrac{2(3s+1)e^{-3s}}{s^2}$$