I'm reading a book on asymptotic methods and I encountered the following ODE, do you have any clue how to solve this? Thanks.
You should try using the complem entary and particular solution.
On the right hand side you have a 2nd order linear DE which can be solved through a standard technique. On the Right hand side you have a particular solution which can be solved using a number of techniques including operator methods (using the d/dx = D as an operator).
These techniques should be taught in any standard differential equations courses.
I see. But when I tried to solve it in this way: I know the left hand side will give me the solution like (with right hand side being set to zero temporally), then I assume and plug it in, but this way seems not to work. In the end, I got sth. like . How to proceed from here? I didn't reduce the problem to a simple one, C still appears with a second order derivative. Do you know any other techniques? Thanks
And it seems not trivial because I just used Mathematica to see the final result, which is attached. I think it involves some advanced technique? It's great if any of you could solve it. I am curious to see the derivation. Thanks.