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How can you solve a system of second order differential equation, which is not time, but length and radius dependent?

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I thnik it cannot be solved by some prebuild ode integrator, like ode45. I tried using 'for loop', but I don't know, how to solve a second order diff.eq. with for cycle. Here is the example I try to model. (Also if you can help me out with the programing of the initial and boundary conditions I would be very glad :) )

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Fabio Freschi
Fabio Freschi el 16 de Sept. de 2021
This is not an ODE but a PDE. you should have a look at pdepe
  4 comentarios
John D'Errico
John D'Errico el 16 de Sept. de 2021
@Jani - This would take a moderate amount of time for someone to write the code for you, far beyond what can be expected of an answer, even using a tool like pdepe. And you would surely want explanations, etc, not just bare code that would be unreadable and unusable. This is why you need to make some serious effort. You might even succeed.
If at some point, you then get stuck, then post a question, showing what you did, and explaining where and why you are stuck. Then you may get additional help. Otherwise, it is asking too much for someone to do your work for you.
Jani el 16 de Sept. de 2021
You're right, thanks for the inspiring comments. I'm gonna try make it work.

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