I'm having some trouble with the attached problem. If anyone could give me a guide as to how I should tackle it, it would be much appriciated.
Regards,
Finnigan.
It is a second order costant coefficient linear inhomogeneous ODE, you find the general solution to the homogeneous equation then add that to a particular integral of the equation.
A particular integral for this will be of the form $\displaystyle a \sin(3x)$