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Anyone have any ideas for a solution to this $$0 = F F''+\left.2F'\right.^2+ xF' + F$$ where primes denote derivatives with respect to ##x##.

So far I have tried this $$0=\left( F F'\right)'+\left({xF}\right)'+\left.F'\right.^2$$

Which obviously failed. I also thought of this $$0 = F^2 F''+2F\left.F'\right.^2+ xFF' + F^2\\

= (F'F^2)' + (xF^2)'+xFF'$$

which also fails. Any ideas? I know an analytic solution exists, but how to derive it?

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# A Help solving non-linear ODE analytically

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