I'm a little rusty on Undetermined Coefficients, but you want to start by arbitrarily choosing a function in the same form as the inhomogeneous one you're giving.

For example, should work for this situation.

Find the derivative, and second derivative so that

and

Now that you have that, you can plug in these functions where they are needed in the original. So, you should get

I'm sort of confused, and maybe you left out a y factor, but if this is right, then you get 0 for both coefficients.

So, assuming that you did write the original equation correctly, then the solution to the inhomogeneous part is as follows:

You can solve for using your typical method of solving for and

If you need help with the homogeneous solution, just post, and I will help you out.