# MATLAB Having a problem with solving a second order ODE equation using Matlab

#### kubekas

I am having a problem coding a Matlab code that solves a second ODE equation which I give below:

x^3*(1-2*x*M)d^2J(x)/dx^2+2*(2*x^2+i*nu*x-7*x^3*M)*dJ(x)/dx
-2*(2*x+8*M*x^2+i*nu)*J(x)=0.

where

M = 1 (Mass of a black hole),
nu = 0.74734+0.17792*i,
J is a function of x,
i represents a complex number.

This equation is very complex to solve. Fistly I tried the Matlab shooting
method and it did not work because this equation is singular at the boundries i.e
0 and 1. Now I am trying to solve it using Matlab Finite Difference Method. I must point out that this problem has no analytic solution and we hope that it can be solved numerically.

Can any one out there help me with this problem.
Thanks
Amos

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