Second Order Equations-Undetermined Coefficients: Problem 3 (1 point) For the differential equation y" + 6y' +9y = -12e-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. y(t) (g) Find the particular solution satisfying y(0) = -4 and y'(0) = 7. y(t) =

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Second Order Equations-Undetermined Coefficients: Problem 3 (1 point) For the differential equation y" + 6y' +9y = -12e-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