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 = 0.211073 (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 = 0.071 (sec), leaf count = 53

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