ODE No. 414

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

\[ x^3+x y'(x)^2+y(x) y'(x)=0 \] Mathematica : cpu = 3599.97 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 1.07 (sec), leaf count = 269

\[ \left \{ \int _{{\it \_b}}^{x}\!{\frac {1}{{\it \_a}} \left ( -y \left ( x \right ) -\sqrt {-4\,{{\it \_a}}^{4}+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( \sqrt {-4\,{{\it \_a}}^{4}+ \left ( y \left ( x \right ) \right ) ^{2}}+5\,y \left ( x \right ) \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!{1 \left ( -2+ \left ( 80\,{\it \_f}+16\,\sqrt {-4\,{x}^{4}+{{\it \_f}}^{2}} \right ) \int _{{\it \_b}}^{x}\!{{{\it \_a}}^{3} \left ( \sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}+5\,{\it \_f} \right ) ^{-2}{\frac {1}{\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}}}}\,{\rm d}{\it \_a} \right ) \left ( \sqrt {-4\,{x}^{4}+{{\it \_f}}^{2}}+5\,{\it \_f} \right ) ^{-1}}{d{\it \_f}}+{\it \_C1}=0,\int _{{\it \_b}}^{x}\!{\frac {1}{{\it \_a}} \left ( -y \left ( x \right ) +\sqrt {-4\,{{\it \_a}}^{4}+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( 5\,y \left ( x \right ) -\sqrt {-4\,{{\it \_a}}^{4}+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!{1 \left ( -2+ \left ( -80\,{\it \_f}+16\,\sqrt {-4\,{x}^{4}+{{\it \_f}}^{2}} \right ) \int _{{\it \_b}}^{x}\!{{{\it \_a}}^{3} \left ( -5\,{\it \_f}+\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}} \right ) ^{-2}{\frac {1}{\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}}}}\,{\rm d}{\it \_a} \right ) \left ( 5\,{\it \_f}-\sqrt {-4\,{x}^{4}+{{\it \_f}}^{2}} \right ) ^{-1}}{d{\it \_f}}+{\it \_C1}=0 \right \} \]