I am trying to solve the following Sturm-Liouville problem. $$(\frac{1}{x^{2m}}\cdot{y'})'+\frac{m(m+1)}{x^{2(m+1)}}\cdot{y}+\lambda\frac{1}{x^{2m}}\cdot{y}=0$$ Re-written as : $$y''-\bigg(\frac{2m}{x}\bigg)y'+\bigg(\frac{m(m+1)}{x^2}+\lambda\bigg)y=0$$.
What type of substitution should be used to solve this ODE? It is cannot be an euler , and cannot figure out how to use a different method.