2.316   ODE No. 316

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

\[ \left (2 \text {Global$\grave { }$x} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^3+\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right ) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2=0 \] Mathematica : cpu = 0.0374485 (sec), leaf count = 48

\[\left \{\{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to 0\},\text {Solve}\left [\text {Global$\grave { }$x}=c_1 e^{-\frac {1}{2} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2}-\frac {1}{4} e^{-\frac {1}{2} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2} \text {Ei}\left (\frac {\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2}{2}\right ),\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right ]\right \}\]

Maple : cpu = 0.058 (sec), leaf count = 53

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