Trial Solution for this Differential Equation

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?

Quote:

---

Originally Posted by zerobladex

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?

---

They are equivalent.