Tricky ODE with an Interesting Presentation Coming from P-Laplace on Schwarzchild Space

Question

I am currently looking at the following ODE: $$2 \frac{y''}{y'}=\frac{\frac{-4}{r}y'-2(p-2)\frac{m}{r^2}(1+\frac{m}{2r})^3}{y'+(p-2)(1+\frac{m}{2r})^4}$$ Does anybody have any examples of standard ODE methods I should be paying particular attention to? I tried to use a perturbation series (letting $p=2+\epsilon$ since we are perturbing away from the standard 2-laplace solution), but I have not had luck getting it into a nice form. The independent variable is r, a radial coordinate, and m,p are constants.