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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