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Solving a system of second order differential equations, with length and radial derivates, but the conditions are quite complex to me.

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I want to use for loop to solve these equations (for drying particles in a fluid bed), but there are two things which prevent me.
1.) I don't know how to write the second order derivate in a for loop
2.) The inital and boundry conditions are somewhat difficult for me to solve. Can you write a script with which it runs. please?


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