2.410   ODE No. 410

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

\[ x y'(x)^2+4 y'(x)-2 y(x)=0 \] Mathematica : cpu = 30.7078 (sec), leaf count = 80

\[\text {Solve}\left [\left \{x=-\frac {2 (2 \text {K$\$$350139}-y(\text {K$\$$350139}))}{\text {K$\$$350139}^2},y(x)=4 e^{-4 \left (\frac {1}{2} \log (2-\text {K$\$$350139})-\frac {\log (\text {K$\$$350139})}{2}\right )} \left (\frac {2}{\text {K$\$$350139}}+\log (\text {K$\$$350139})\right )+c_1 e^{-4 \left (\frac {1}{2} \log (2-\text {K$\$$350139})-\frac {\log (\text {K$\$$350139})}{2}\right )}\right \},\{y(x),\text {K$\$$350139}\}\right ]\] Maple : cpu = 0.24 (sec), leaf count = 64

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