What is a numerical method to solve IVP at irregular singular point?

108 Views Asked by At

I have tried to search for numerical method to solve IVP with irregular singular point but didn't find any.

What is the proper method I can use to solve such equations?

$$y''+\frac{y'}{x^2}+y=x^3+6x+3$$ With initial conditions $$y(0)=0, y'(0)=0$$

Obviously, collocation method (which I know) won't work.

I'm not interested in this particular problem, it's only an example.