2.385   ODE No. 385

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

\[ -2 x^2 y'(x)+y'(x)^2+2 x y(x)=0 \] Mathematica : cpu = 301.968 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 0.535 (sec), leaf count = 169

\[ \left \{ y \left ( x \right ) ={\frac {{x}^{4}- \left ( {\it RootOf} \left ( {x}^{16}-12\,{{\it \_Z}}^{2}{x}^{12}+16\,{{\it \_Z}}^{3}{x}^{10}+30\,{{\it \_Z}}^{4}{x}^{8}-96\,{{\it \_Z}}^{5}{x}^{6}+100\,{{\it \_Z}}^{6}{x}^{4}-48\,{{\it \_Z}}^{7}{x}^{2}+9\,{{\it \_Z}}^{8}-16\,{\it \_C1}\,{x}^{4} \right ) \right ) ^{2}}{2\,x}},y \left ( x \right ) ={\frac {{x}^{4}- \left ( {\it RootOf} \left ( {\it \_C1}\,{x}^{16}-12\,{\it \_C1}\,{{\it \_Z}}^{2}{x}^{12}-16\,{\it \_C1}\,{{\it \_Z}}^{3}{x}^{10}+30\,{\it \_C1}\,{{\it \_Z}}^{4}{x}^{8}+96\,{\it \_C1}\,{{\it \_Z}}^{5}{x}^{6}+100\,{\it \_C1}\,{{\it \_Z}}^{6}{x}^{4}+48\,{\it \_C1}\,{{\it \_Z}}^{7}{x}^{2}+9\,{\it \_C1}\,{{\it \_Z}}^{8}-16\,{x}^{4} \right ) \right ) ^{2}}{2\,x}} \right \} \]