Solve Troesch's Equation: Numerical Technique & Derivation

[wasi-uz-zaman]

TL;DR

Troesch's equation explanation

hi, i am going to solve Troesch's equation u′′(x) = λ sinh(λu(x))
by numerical technique, but i couldn't find the derivation of it- kindly anyone knows its derivation or details of variable used.
regards wasi

 

[Baluncore]

Here is an introduction, a solution and a bibliography.
https://www.researchgate.net/publication/253644077_A_general_solution_for_Troesch's_problem/link/55a9969208ae815a04254f47/download