Solving System of DEs: T, u, phi w/ Constants & r

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This discussion focuses on solving a system of differential equations (DEs) involving the dependent variables T, u, and phi, with r as the independent variable. The user, MoMo, seeks assistance in determining whether a closed-form solution exists for these equations. The mention of "separation of variables" suggests a potential method for solving the DEs, although no specific equations were provided in the discussion.

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msenousy
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Hello dear all;
I have been trying to solve a system of DE for a long time; however, I find it difficult to solve it.
I am wondering if anyone can help me in solving them ir at least telling me whether they have a closed form solution or not.

the equations are attached to this mail in a jpg format

The dependent variables are, "T", "u", and "phi"
the dependent variable is "r"
other than that everything is constant

Thanks;
MoMo
 

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