Linear Differential Equations

Please help. I need it asap.

Solve the linear differential equation:
(D5–12D4+52D3–112D2+192D–256)y = 0

When I factored it out. I got (D-4)^3 (D^2 +4)

With D-4..

My equation will be Y= (C1 + C2x + C3x^2)e^4x

But how about my D^2 + 4?

How can I add that in my equation?

Infinitesimal's picture

D^2 +4 will actually be $C_4 \cos 2x + C_5 \sin 2x$