Second Order Equations-Nonhomogeneous Linear: Problem 1

(1 point)

For the differential equation y" - 2y - 3y = 7 - 3t

(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 y2, 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.)

yn (t)=

(e) Find a particular solution of the above non-homogeneous differential equation.

Up (t)

(f) State the general solution of the above non-homogeneous differential equation.

y(t) =

(g) Find the particular solution satisfying y(0) = -9 and y'(0) = 3.

Y(t)