3.316   ODE No. 316

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

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

Mathematica: cpu = 0.039005 (sec), leaf count = 48 \[ \left \{\{y(x)\to 0\},\text {Solve}\left [x=c_1 e^{-\frac {1}{2} y(x)^2}-\frac {1}{4} e^{-\frac {1}{2} y(x)^2} \text {Ei}\left (\frac {y(x)^2}{2}\right ),y(x)\right ]\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 53 \[ \left \{ y \left ( x \right ) =0,y \left ( x \right ) =\sqrt {-2\,{\it RootOf} \left ( {{\rm e}^{{\it \_Z}}}{\it Ei} \left ( 1,{\it \_Z} \right ) +4\,{{\rm e}^{{\it \_Z}}}{\it \_C1}-4\,x \right ) },y \left ( x \right ) =-\sqrt {-2\,{\it RootOf} \left ( {{\rm e}^{{\it \_Z}}}{\it Ei } \left ( 1,{\it \_Z} \right ) +4\,{{\rm e}^{{\it \_Z}}}{\it \_C1}-4\,x \right ) } \right \} \]