Using complex numbers for 2nd order DE
I can change this equation, using Eulers method, and get the answers using and , but using complex numbers is apparently faster and we have to do it this way for my professor...so if you could help me figure this out I would appreciate it.
HERE IS WHAT I DID:
First, I'll solve the homogeneous case to find the complementary solution and the roots.
Now, to find the solution , where is the particular solution to the non-homogeneous equation, I need help. I guessed a few functions but none seemed to work out.
Here is what Ive tried:
Since ...well the real part I think
is a root of the homogenous equatoin, so I need multiply my guess for by
From here I cannot figure out what function I need to use...