2.410   ODE No. 410

\[ x y'(x)^2+4 y'(x)-2 y(x)=0 \] Mathematica : cpu = 30.724 (sec), leaf count = 90


\[\text {Solve}\left [\left \{x=-\frac {2 (2 K[1]-y(K[1]))}{K[1]^2},y(x)=4 \left (\frac {2}{K[1]}+\log (K[1])\right ) \exp \left (-4 \left (\frac {1}{2} \log (2-K[1])-\frac {1}{2} \log (K[1])\right )\right )+c_1 \exp \left (-4 \left (\frac {1}{2} \log (2-K[1])-\frac {1}{2} \log (K[1])\right )\right )\right \},\{y(x),K[1]\}\right ]\] Maple : cpu = 0.177 (sec), leaf count = 64


\[y \relax (x ) = \frac {x \,{\mathrm e}^{2 \RootOf \left (-x \,{\mathrm e}^{2 \textit {\_Z}}+4 x \,{\mathrm e}^{\textit {\_Z}}-4 \,{\mathrm e}^{\textit {\_Z}}+c_{1}+8 \textit {\_Z} -4 x \right )}}{2}+2 \,{\mathrm e}^{\RootOf \left (-x \,{\mathrm e}^{2 \textit {\_Z}}+4 x \,{\mathrm e}^{\textit {\_Z}}-4 \,{\mathrm e}^{\textit {\_Z}}+c_{1}+8 \textit {\_Z} -4 x \right )}\]