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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

5 votes
2 answers
553 views

An ordinary differential equation

While I was working on a variational problem, I met this equation as its Euler-Lagrange equation, but I cannot solve it: $ x= \frac{af'(x)}{\sqrt{1+af'(x)^{2}}} + \frac{bf'(x)}{\sqrt{1+bf'(x)^{2}}} \ …