Solve the Differential equation by inspection

Question

d^2q/dt^2 + 64 q = -32

Answer 1

q'' + 64q = 32;

Characteristic equation: r² + 64 = 0; r = ±8i; q_GH = Acos8t + Bsin8t

q_P = M; q_p' = qP'' = 0; 64M = -32, M = -1/2

q = Acos8t + Bsin8t -1/2