This is on a review sheet for the exam, and I have the solution, but I can't figure out how the professor got to the first step.
The question reads: Find the general solution to:
[(x^2)/2]y'' + 2xy' - (7/8)y = (x^4)/2 x>0
The first line on the solution sheet reads:
Characteristic eq: (1/2)r(r-1) + 2r - (7/8) = 0
I understand the substituting r for y's, but I don't see how he was able to get rid of the x's and get the r(r-1) part.
It would help a ton if someone could explain this to me.
Thanks a lot in advance.
May be that the best approach is to 'attack' first the 'incomplete equation'...
The 'coefficients' of this linear DE aren't constants , so that the 'standard approach' doesn't work. It is easy to verify that solutions of (1) are of the type ... then try to find the constants able to solve (1)...