Where m = ω = h = c1 = x0 = constants
I'm trying to solve a second order differential equation with non-constant coefficients and I using series to solve for it. I've plugged in the series solution and have simplified it down to the above equation. I have gotten everything to be represented in x^k, but I can't get the series in the second and third term to start from the same index without writing out some terms.
I want to represent everything in one series with x^k so that I can equate the coefficients equal to zero. Then I can find the reoccurance relation to find what A_k equals to for the solution to the differential equation I'm trying to solve.
Is it possible to solve for A_k?