There are initial conditions to but once I get the general solution i'll be away!Find the solution to:

The auxiliary equation is:

Hence

This is for the homoegeneous case so now we need to find a part that gives on the RHS.

Let

Then:

Unfortunately this gives:

Everything comes out zero. I can't see what i'm doing wrong here, the fact all the constants are zero suggests that the equation I am trying (ie. is wrong but i'm not sure what I can change it into.