Second Order Equations-Nonhomogeneous Linear: Problem 2 (1 point) For the differential equation y" - 3y - 54y= 161 + 66t + 108t² (a) State the characteristic polynomial for the differential equation. (Use the variable r.) (b) List the roots of the characteristic polynomial. (c) List y₁ and y/2, a fundamental set of solutions of the complementary homogeneous equation. (d) Find the general solution of the complementary homogeneous equation. (In your answer, use A and B to denote the arbitrary constants.) U₁ (t) = (e) Find a particular solution of the above non-homogeneous differential equation. yp (t) = (f) State the general solution of the above non-homogeneous differential equation. Y(t) = (g) Find the particular solution satisfying y(0) = -10 and y'(0) = -19. y(t):

Fig: 1