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

[msenousy]

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

Thanks;
MoMo

 

[Clausius2]

Separation of variables?

 

[tacman]

Hello MoMo,

Solving systems of differential equations can be a challenging task, but with the right approach, it is definitely possible. It would be helpful if you could provide more information about the specific equations you are trying to solve, such as their order and boundary conditions. This would allow us to better understand the problem and provide more specific advice.

In general, there are a few methods that can be used to solve systems of DEs. One approach is to use substitution, where you solve for one variable and then substitute it into the other equations. Another approach is to use elimination, where you eliminate one variable at a time until you are left with a single equation to solve.

It is also important to note that not all systems of DEs have closed form solutions. In some cases, numerical methods may be necessary to approximate the solutions. However, it is worth exploring different techniques and methods to see if a closed form solution can be found.

I would suggest consulting with a math tutor or reaching out to online forums and communities for additional help and guidance in solving your system of DEs. Good luck!