I'm having trouble figuring out the trial solution for this particular differential equation:
y'' + 9y = (x^2)* sin x
I wrote the trial solution as being (Ax^2 + Bx + C)(D cos x + E sin x)
However my book writes it as being
(Ax^2 + Bx + C)cos x + (Ex^2 + Fx + G) sin x
Can someone explain to me why this is?