3.220   ODE No. 220

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

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

Mathematica: cpu = 0.012002 (sec), leaf count = 57 \[ \left \{\left \{y(x)\to -\sqrt {c_1 e^{\frac {x^2}{2}}-x^2-2}\right \},\left \{y(x)\to \sqrt {c_1 e^{\frac {x^2}{2}}-x^2-2}\right \}\right \} \]

Maple: cpu = 0.016 (sec), leaf count = 43 \[ \left \{ y \left ( x \right ) =\sqrt {{{\rm e}^{{\frac {{x}^{2}}{2}}}}{ \it \_C1}-{x}^{2}-2},y \left ( x \right ) =-\sqrt {{{\rm e}^{{\frac {{x} ^{2}}{2}}}}{\it \_C1}-{x}^{2}-2} \right \} \]