This paper shows, for the first time, that the explicit and exact solution to the Troesch nonlinear two-point boundary value problem may be computed in a direct and straightforward fashion from the general solution obtained by a generalized Sundman transformation for the related differential equation, which appeared with the sinh-Poisson and Poisson-Boltzmann equations to be special cases of a more general equation. As a result, various initial and boundary value problems for these equations may be solved explicitly and exactly.
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