3.396   ODE No. 396

\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+y \left ( x \right ) \left ( y \left ( x \right ) -x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -x \left ( y \left ( x \right ) \right ) ^{3}=0} \]

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

Mathematica: cpu = 0.014002 (sec), leaf count = 29 \[ \left \{\left \{y(x)\to \frac {1}{x-c_1}\right \},\left \{y(x)\to c_1 e^{\frac {x^2}{2}}\right \}\right \} \]

Maple: cpu = 0.016 (sec), leaf count = 20 \[ \left \{ y \left ( x \right ) = \left ( x+{\it \_C1} \right ) ^{-1},y \left ( x \right ) ={{\rm e}^{{\frac {{x}^{2}}{2}}}}{\it \_C1} \right \} \]