For the differential equation y 5y 4y 88e7t a State the characteristic polynomial for the differential equation b List the roots of the characteristic polynomial c List y and y2 d Find the homogeneous solution to the differential equation In your answer use A and B to denote the arbitrary constants Y t e Find the non homogeneous solution to the differential equation Y t f State the general solution y t g Find the particular solution satisfying y 0 3 and y 0 8 y t