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 = 30.8569 (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 = 0.125 (sec), leaf count = 64

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