Question: Cannot find the solution of a non-linear equation with hyperbolic trigonometric term

In solving the brachistochrone for a fine string of length L under the pull of g passing through the point (0,0) and (a,b) using the euler-lagange method,I stumble on this non-linear relation:


which I need to solve for C.

Maple give me the famous RootOf:

RootOf(A*exp(_Z)^2 - 2*_Z*L*exp(_Z) - A)

where A = mu*g*a

Can it be solve for C or am I force to use numeric method?

Thank you in advance for your help.


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