Any tips on how to solve complicated simultaneous equations?

Hello @anyone who has any advice

I'm super stuck at this simultaneous equation,

By varying ℓ, I'm trying to solve for Φm and 𝑥m, while everything else are constants.

but its so complicated and I don't know how to input these into matrices (AX =B) to solve for inverse A\B.

Any help or advice would be greatly appreciated!!

[KSSV]

Have a look on symbolic toolbox.

[Walter Roberson]

Those are non-linear. There is no hope of solving them using the \ operator.

You do not have matrices in any apparent way.

Are there any constraints that you can give on the constants? Potentially dealing with some complex-valued cases might be ruled out.

[David Lee]

Yes, this is part of a heat transfer problem, the constraints are all positive real values. For now, I'll try using the symbolic toolbox. Thanks for your replies! :-)

[Walter Roberson]

You are probably going to need to proceed numerically using fsolve() . Subtract one side of each equation from the other, to get a resulting expression that must equal zero. Now fsolve() a function that calculates the two different expressions.

If you use the symbolic toolbox, you can simplify. Solving the first expression for gives an hyperbolic arc cosine expression that is not unresonably long; you can then substitute that into the second equation to get a single equation in one variable