Hello!

I having problems getting started with this problem:

Using subn and rewrite:

hence find all solutions.

When I perform the substitution using and , I get:

I can't find any complimentary functions and probably due to my undergrad engineering major, I tried a Laplace transform, but end up with a horrible function owing to the part that would leave a on the LHS- I suspect this is not be the correct method as alluded to within the question - there must be a reason for the subn.....

I can't use an order reduction or variation of parameters as I don't have an already known solution- unless I use a trial and error! If anyone can kick me in the right direction, I will be most greatful.... I can't seem to see through it right now!

Thanks for looking!