The question asks me to solve x^2 y'' - 5x y' - 7y = x^3 as function of x. In other words, it's asking for y(x). I am given the initial conditions y(1) = 10 and y'(1) = 8.
Someone who wasn't very sure told me to use characteristic equations and the method of undetermined coefficients but is that correct? If so, how do I set it up mechanically? I only know how to use characteristic equations when there are no x variables in the differential equation. I am really, really stuck. I only divided both sides by x^2.
The answer is:
If someone could show me how to set up the problem (tedious steps aren't necessary), I would greatly appreciate it!
Thanks in advance!