2.410   ODE No. 410

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

\[ \text {Global$\grave { }$x} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2+4 \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})-2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})=0 \] Mathematica : cpu = 31.0199 (sec), leaf count = 80

\[\text {Solve}\left [\left \{\text {Global$\grave { }$x}=-\frac {2 (2 \text {K$\$$1863398}-\text {Global$\grave { }$y}(\text {K$\$$1863398}))}{\text {K$\$$1863398}^2},\text {Global$\grave { }$y}(\text {Global$\grave { }$x})=c_1 e^{-4 \left (\frac {1}{2} \log (2-\text {K$\$$1863398})-\frac {\log (\text {K$\$$1863398})}{2}\right )}+4 e^{-4 \left (\frac {1}{2} \log (2-\text {K$\$$1863398})-\frac {\log (\text {K$\$$1863398})}{2}\right )} \left (\frac {2}{\text {K$\$$1863398}}+\log (\text {K$\$$1863398})\right )\right \},\{\text {Global$\grave { }$y}(\text {Global$\grave { }$x}),\text {K$\$$1863398}\}\right ]\]

Maple : cpu = 0.057 (sec), leaf count = 64

\[ \left \{ y \left ( x \right ) ={\frac {x{{\rm e}^{2\,{\it RootOf} \left ( -x{{\rm e}^{2\,{\it \_Z}}}+4\,x{{\rm e}^{{\it \_Z}}}-4\,{{\rm e}^{{\it \_Z}}}+{\it \_C1}+8\,{\it \_Z}-4\,x \right ) }}}{2}}+2\,{{\rm e}^{{\it RootOf} \left ( -x{{\rm e}^{2\,{\it \_Z}}}+4\,x{{\rm e}^{{\it \_Z}}}-4\,{{\rm e}^{{\it \_Z}}}+{\it \_C1}+8\,{\it \_Z}-4\,x \right ) }} \right \} \]