(1 point)
For the differential equation y" - 10y +25y = 85 - 25t
(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.
yp (t) =
(f) State the general solution of the above non-homogeneous differential equation.
y(t) =
(g) Find the particular solution satisfying y(0) = 0 and y'(0) = -24.
y(t) =
Fig: 1