Homework: Discontinuous SourcesConsider the initial value problem for function y(t) given by,y''-2y'-3y=2u(t-4)e2t,y(0)=0,y'(0)=0where u(t-c) denotes the step function with step att=c.Part 1: Finding F(s)(a) Find the Laplace Transform of the source function, F(s)=L[2u(t-4)e2t].F(s)=Note: We are asking for F(s)=L[2u(t-4)e2t], not for Y(s)=L[y(t)].Hints:Rewrite the exponential ase2t=e2(t-t0+t0) for an appropriate value oft0.Use the exponential property ea+b=eaeb for a=2(t-t0) and b=2t0.Part 2: Finding Y(s)(b) Find the Laplace Transform of the solution, Y(s)=L[y(t)].Y(s)=Note: We are asking for Y(s)=L[y(t)], not for y(t).Part 3: Rewriting Y(s)(c) The function Y(s) found in part (b) has a partial fraction decompositionY(s)=e-4s(A(s-a)+B(s-b)+C(s-c))where we assume that a>b>c. Find the constants A,B,C,a,b, and c.A=,B=a=bar()>b=,bar()>c=Recall: In your answer a>b>c.Part 4: Finding y(t)