For nonhomogenous linear DE, y''+9y=sin(3x), using method of undetermined coefficients, I get 0 = sin(3x) when plugging in my trial particular solution (Asin3x +Bcos3x). Am I doing this wrong? If not, what do i do next?

Question

For nonhomogenous linear DE, y''+9y=sin(3x), using method of undetermined coefficients, I get 0 = sin(3x) when plugging in my trial particular solution (Asin3x +Bcos3x).  Am I doing this wrong?  If not, what do i do next?

anonymous · Answer

never mind, i realized my problem

anonymous · Answer

So you multiplied your trial solution by x and went through the motions?  Did you get a particular solution of $$y=-\frac{1}{6}x \cos 3 x$$?

anonymous · Answer

yes, that's what i got. thanks!