non-homogeneous guessing question

[Weina Zhu]

during solving the general solution for the non-homogeneous equation, why should we guessing an answer combine sin&cos together for
an equation like the right-hand side only contains one of the sin&cos.

Thanks!

[Victor Ivrii]

Because derivative of sine is cosine and v.v. Try to solve $y''+y'=\cos(x)$ as with $y=a\cos(x)$.