Second Order Equations-Undetermined Coefficients: Problem 5

(1 point)

Consider the differential equation y" + 2y' - 3y = (6 + 4t - 24t²) e-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.)

Yr(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.

v(t) =

(g) Find the particular solution satisfying y(0) = -5 and y' (0) = -2.

-0

y(t) =