second order equations nonhomogeneous linear problem 2 1 point for the
Second Order Equations-Nonhomogeneous Linear: Problem 2
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.
(g) Find the particular solution satisfying y(0) = -10 and y'(0) = -19.
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