Solving a system of differential equations in T, u, and phi

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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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