8.180   ODE No. 1770

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

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

Mathematica: cpu = 0.792101 (sec), leaf count = 28 \[ \left \{\left \{y(x)\to \frac {1}{x^2 \left (-\frac {c_1}{x}+c_2-\frac {1}{x^2}\right )}+1\right \}\right \} \]

Maple: cpu = 1.560 (sec), leaf count = 26 \[ \left \{ y \left ( x \right ) ={\frac {x \left ( {\it \_C1}\,x-{\it \_C2} \right ) }{{\it \_C1}\,{x}^{2}-{\it \_C2}\,x-1}} \right \} \]