Problem 4: Consider the differential equation y + 6y + 5y = 36(t- 4) with initial conditions y(0) = 5 and y (0) = 2. a) Take the Laplace transform of the differential equation and solve for Y($). Use partial fraction expansion (PFE) to simplify your answer. Solution: [Insert your math/explanation here.] b) Find the solution of the differential equation by computing y(1) = F-( Y(s)). Solution: [Insert your math/explanation here.] c) Use MATLAB to plot your solution for time f = 0 to f = 10. Solution: * [Insert your MATLAB code and plot here. ] d) Use the MATLAB dsolve() function to solve the system of equations and plot your solution on a new figure. The result provided by dsolve() and your solution from above should match. Solution: * [Insert your MATLAB code and plot here. ]