Consider the initial value problem for function y given by,y''-7y'12y=5u(t-4),y(0)=0,y'(0)=0where u(t-c) denotes the step function with step at t=c.Part 1: Finding F(s)(a) Find the Laplace Transform of the source function, F(s)=[5u(t-4)].F(s)=Note: We trure asking for F(s)=[5u(t-4)], not for Y(s)=[y(t)].Part 2: Finding Y(s)(b) Find the Laplace Transform of the solution, Y(s)=[y(t)].Y(s)=5e-4(s)s(s2-7(s)12)Note: We are asking for Y(s)=[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(AsB(s-b)C(s-c))where we assume that b>c. Find the constants A,B,C,b, and c.A=B=C=b=Recall: In your answer b>c.