Given the differential equation:

Find the solution when

Hint:

The answer should be:

My attempt (I'm not sure if I'm using the correct method):

I start by using the "guessing method" which states that if you have then you can guess on the solution with the form:

So my guess so far is:

I hereby differentiate this guess 2 and 4 times and insert it to my original equation:

Inserted:

I clean it up a little:

This is as far as I've made it because in the examples in my textbook, they have not shown what to do when appears in the original equation, thus I have no idea how to isolate and find the values of and .

Can somebody please tell me if I'm on right track at all, and if so, what do I do next?