MATLAB solving BVP using bvp4c, variable coefficient

Say I have an bvp that involve the equation below

If I was to have enough boundary conditions to satisfy ODE, would it be possible to solve the equation simultaneously in order to get a solution for the equation?

Ideally would be a constant coefficient, but as seen with the solutions I am currently getting I'm wondering if the physics involving the currently considered constant coefficient equation describes the physics incorrectly. I would like to see how the now variable coefficient "" changes in order to get the to fit my boundary conditions.

Any information or examples would be greatly appreicated!

Answer 1

[Torsten]

If you make the ansatz

f ( r ) = a0 + a1*r + a2*r^2 + ...+ an *r^n

you will need (n+1) additional boundary conditions to fix the coefficients ai.