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

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

lemelinm 1535 Maple
solve brachistochrone
September 13 2022
1

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:

C*sinh(mu*g*a/C)=L

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.

Mario
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