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I am trying to solve the differential equation

$2y^2 + 2 x y y' + x y^3 y' - 2 x^2 (y')^2 + x^2 y y'' = 0$

I tried 

DSolve[2 y[x]^2 + 2 xy[x] Derivative[1][y][x] + 
x y[x]^3 Derivative[1][y][x] - 2 x^2 Derivative[1][y][x]^2 + 
x^2 y[x] (y^\[Prime]\[Prime])[x] == 0, y[x], x]

but I get the error message

Attributes::notfound: Symbol DSolveDispatchODE not found.
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  • $\begingroup$ Likely due to a missing space in xy[x]. When I replace it with x y[x], after some time Mathematica returns the command, which means that Mathematica can not find a closed form for the solution (which then very likely does not exist). $\endgroup$
    – Fred Simons
    Commented Nov 17, 2015 at 18:06
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    $\begingroup$ the way you have expressed the second derivative is not correct, although that might be a typo here. ( Try D[y[x],{x,2}] ) (Fixing that and the space it just returns unevaluated indicating, not surprisingly, that DSolve doesn't know how to solve it ) $\endgroup$
    – george2079
    Commented Nov 17, 2015 at 18:08

1 Answer 1

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you can try this: 

eq = 2 y[x]^2 + 2 x*y[x]*y'[x] + x*y[x]^3*y'[x] - 2 x^2*y'[x]^2 +x^2*y[x]*y''[x] == 0;
DSolve[eq, y, x]
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  • $\begingroup$ This didn't work for me, it just outputted as DSolve [....] $\endgroup$
    – supercoolphysicist
    Commented Nov 24, 2015 at 14:55
  • $\begingroup$ I think it means that mathematica couldn't solve that analytically, with NDSolve you see this answer: y-> InterpolatingFunction $\endgroup$
    – jack cilba
    Commented Nov 24, 2015 at 16:47

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