3. To solve differential equations with Laplace transforms, we use the fact that L{y}=s2Ysy(0)s(0). In this problem, we will derive that result. (a) (4 points) By definition, the Laplace transform of y(t) is L{y(t)}=0y(t)estdt Use this to show that L{y}=sL{y}y(0). Hint: integration by parts. (b) (2 points) Now, use part (a) and the fact that y=(y) to derive the result. You should not use the definition of the Laplace transform again in this part, and you should not be dealing with any integrals