Hey guys, I am a little stuck/unsure in an assignment for my signals and systems course. My working is attached. I have established the DE, but I am unsure whether or not I have solved the DE correctly. I used the method of undetermined coefficients. I have found the same solution in a Rao textbook on vibrations, but the solution varies slightly, but I'm not sure why because not all the steps are explained and I can't seem to figure out why. Any help would be appreciated, thank you!