Can the method of undetermined coefficients be applied here?

[Precursor]

Homework Statement
Decide whether or not the method of indetermined coefficients can be applied to find a particular solution of the given equation:

The attempt at a solution
I think the answer is yes, because the equation is of the form: $$a\ddot{y}+b\dot{y}+cy=F(t)$$where F(t) is the sum or product of polynomials, exponentials, sines, cosines.

Am I correct?

 

[rock.freak667]

Yes it can, you can also factor out the 4x to make it easier since you know what sin²x+cos² is equal to.

 

[Precursor]

Oh so I can replace sin²x+cos²x with 1, which gives me a RHS of simply 4x?

 

[rock.freak667]

Yep.