Solution to diff eq Check whether the function $y=\sin(3x)/3$ is a solution of $xy'+y+3\cos3x$ with the initial condition $y(\pi)=0$ 
Find $xy'$ for the function $y=\sin(3x)/3$
I am a ex-math minor who is just trying to get through this summer class. My professor told us nothing about these. Any help would be awesome! 

Hint
If $y=\frac{\sin(3x)}{3}$, then $y'=\cos(3x)$. So replacing in the expression $$xy'+y+3\cos(3x)=x\cos(3x)+\frac{\sin(3x)}{3}+3\cos(3x)$$ cannot be zero. So $y=\frac{\sin(3x)}{3}$ is not a solution of the differential equation.
For the second part of the problem, assuming that $$xy'+y+3\cos(3x)=0$$ you are asked for $xy'$. Isolate this term from the equation and replace $y$ by its given expression.
I am sure that you can take from here.
