2.416   ODE No. 416

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

\[ x y'(x)^2+(y(x)-3 x) y'(x)+y(x)=0 \] Mathematica : cpu = 301.06 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 0.118 (sec), leaf count = 136

\[ \left \{ -{\frac {{\it \_C1}}{x} \left ( -y \left ( x \right ) +5\,x+\sqrt {9\,{x}^{2}-10\,xy \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( {\frac {1}{x} \left ( -y \left ( x \right ) +3\,x+\sqrt {9\,{x}^{2}-10\,xy \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}} \right ) } \right ) ^{-{\frac {3}{2}}}}+x=0,{\frac {{\it \_C1}}{x} \left ( y \left ( x \right ) -5\,x+\sqrt {9\,{x}^{2}-10\,xy \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( {\frac {1}{x} \left ( -2\,y \left ( x \right ) +6\,x-2\,\sqrt {9\,{x}^{2}-10\,xy \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}} \right ) } \right ) ^{-{\frac {3}{2}}}}+x=0,y \left ( x \right ) =x \right \} \]