2.409   ODE No. 409

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

\[ \text {Global$\grave { }$x} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2-2 \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})-\text {Global$\grave { }$y}(\text {Global$\grave { }$x})=0 \] Mathematica : cpu = 30.7642 (sec), leaf count = 66

\[\text {Solve}\left [\left \{\text {Global$\grave { }$x}=\frac {\text {Global$\grave { }$y}(\text {K$\$$1862933})+2 \text {K$\$$1862933}}{\text {K$\$$1862933}^2},\text {Global$\grave { }$y}(\text {Global$\grave { }$x})=c_1 e^{2 (\log (\text {K$\$$1862933})-\log (1-\text {K$\$$1862933}))}+e^{2 (\log (\text {K$\$$1862933})-\log (1-\text {K$\$$1862933}))} \left (-\frac {2}{\text {K$\$$1862933}}-2 \log (\text {K$\$$1862933})\right )\right \},\{\text {Global$\grave { }$y}(\text {Global$\grave { }$x}),\text {K$\$$1862933}\}\right ]\]

Maple : cpu = 0.055 (sec), leaf count = 63

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