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I'm curious about the nonlinear ODEs with an quotient including dependent variable : $$y''(x)+\frac{Ay(x)x}{1+y(x)}+Bx=0$$ Could you give me a clue on solving this equation explicitly?

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Did you create this ODE yourself? Because in general ODEs have no explicit solution. Well if you found it in a textbook it is another problem... – Sebastien B Jan 31 at 14:48
@Sebastien B yes, I modified the question form $$y''(x)+Ay(x)x+B=0.$$ After your response, I see that it was not clever:( Is such a solution only numerically possible? – pcepkin Feb 1 at 9:32
About your equation $y''(x)+\frac{Ay(x)x}{1+y(x)}+Bx=0$, I honestly have no idea whether there is or not an explicit solution. I can just tell you I don't see an obvious solution... – Sebastien B Feb 1 at 10:59

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