2.414   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 = 0 (sec), leaf count = 0 , timed out

timed out

Maple : cpu = 0.2 (sec), leaf count = 337

\[ \left \{ \int _{{\it \_b}}^{x}\!-{\frac {1}{{\it \_a}} \left ( y \left ( x \right ) +\sqrt {-4\,{{\it \_a}}^{4}+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( \sqrt {-4\,{{\it \_a}}^{4}+ \left ( y \left ( x \right ) \right ) ^{2}}+5\,y \left ( x \right ) \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!2\,{\frac {1}{\sqrt {-4\,{x}^{4}+{{\it \_f}}^{2}}+5\,{\it \_f}} \left ( 8\,\int _{{\it \_b}}^{x}\!{\frac {{{\it \_a}}^{3}}{ \left ( \sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}+5\,{\it \_f} \right ) ^{2}\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}}}\,{\rm d}{\it \_a}\sqrt {-4\,{x}^{4}+{{\it \_f}}^{2}}+40\,\int _{{\it \_b}}^{x}\!{\frac {{{\it \_a}}^{3}}{ \left ( \sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}+5\,{\it \_f} \right ) ^{2}\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}}}\,{\rm d}{\it \_a}{\it \_f}-1 \right ) }{d{\it \_f}}+{\it \_C1}=0,\int _{{\it \_b}}^{x}\!-{\frac {1}{{\it \_a}} \left ( -y \left ( x \right ) +\sqrt {-4\,{{\it \_a}}^{4}+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( -5\,y \left ( x \right ) +\sqrt {-4\,{{\it \_a}}^{4}+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!-2\,{\frac {1}{-5\,{\it \_f}+\sqrt {-4\,{x}^{4}+{{\it \_f}}^{2}}} \left ( 8\,\int _{{\it \_b}}^{x}\!{\frac {{{\it \_a}}^{3}}{ \left ( -5\,{\it \_f}+\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}} \right ) ^{2}\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}}}\,{\rm d}{\it \_a}\sqrt {-4\,{x}^{4}+{{\it \_f}}^{2}}-40\,\int _{{\it \_b}}^{x}\!{\frac {{{\it \_a}}^{3}}{ \left ( -5\,{\it \_f}+\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}} \right ) ^{2}\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}}}\,{\rm d}{\it \_a}{\it \_f}-1 \right ) }{d{\it \_f}}+{\it \_C1}=0 \right \} \]