3.506   ODE No. 506

\[ \boxed { {x}^{2} \left ( x \left ( y \left ( x \right ) \right ) ^{2}-1 \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2} \left ( y \left ( x \right ) -x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2} \left ( {x}^{2}y \left ( x \right ) -1 \right ) =0} \]

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 47.848076 (sec), leaf count = 58 \[ \text {DSolve}\left [2 x^2 (y(x)-x) y(x)^2 y'(x)+x^2 \left (x y(x)^2-1\right ) y'(x)^2-\left (x^2 y(x)-1\right ) y(x)^2=0,y(x),x\right ] \]

Maple: cpu = 1.310 (sec), leaf count = 0 \[ \text {could not solve} \]