2.316   ODE No. 316

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

\[ \left (2 x y(x)^3+y(x)\right ) y'(x)+2 y(x)^2=0 \] Mathematica : cpu = 0.130987 (sec), leaf count = 48

\[\left \{\{y(x)\to 0\},\text {Solve}\left [x=-\frac {1}{4} e^{-\frac {1}{2} y(x)^2} \text {Ei}\left (\frac {y(x)^2}{2}\right )+c_1 e^{-\frac {1}{2} y(x)^2},y(x)\right ]\right \}\] Maple : cpu = 0.043 (sec), leaf count = 53

\[ \left \{ y \left ( x \right ) =0,y \left ( x \right ) =\sqrt {-2\,{\it RootOf} \left ( {{\rm e}^{{\it \_Z}}}{\it Ei} \left ( 1,{\it \_Z} \right ) +4\,{{\rm e}^{{\it \_Z}}}{\it \_C1}-4\,x \right ) },y \left ( x \right ) =-\sqrt {-2\,{\it RootOf} \left ( {{\rm e}^{{\it \_Z}}}{\it Ei} \left ( 1,{\it \_Z} \right ) +4\,{{\rm e}^{{\it \_Z}}}{\it \_C1}-4\,x \right ) } \right \} \]