Solve the following initial value problemy′′ + 9y = 3 cos(3x), y(0) = 0, y′(0) = 0 and write the final solution using real valued functions. Sketch the graph of the solution in a x-y diagram.

Can someone help me solve this?

This is what i done so far

y′′ + 9y - 3 cos(3x)= 0

z^2 +9z -3 cos(3x)= 0

z^2+6z+3z -3cos(3x)=0

z(z+6) + 3(z-cos(3x))=0

(z+3)(z+6)(z-cos(3x))=0

Now im really stuck on what to do. Please help. Thanks.