3.414   ODE No. 414

\[ \boxed { x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +{x}^{3}=0} \]

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

Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]

Maple: cpu = 0.639 (sec), leaf count = 337 \[ \left \{ \int _{{\it \_b}}^{x}\!-{\frac {1}{{\it \_a}} \left ( y \left ( x \right ) +\sqrt {-4\,{{\it \_a}}^{4}+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( \sqrt {-4\,{{\it \_a}}^{4}+ \left ( y \left ( x \right ) \right ) ^{2}}+5\,y \left ( x \right ) \right ) ^{-1}} \,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!2\,{\frac {1}{\sqrt {- 4\,{x}^{4}+{{\it \_f}}^{2}}+5\,{\it \_f}} \left ( 8\,\int _{{\it \_b}}^{ x}\!{\frac {{{\it \_a}}^{3}}{ \left ( \sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}+5\,{\it \_f} \right ) ^{2}\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}}}\,{\rm d}{\it \_a}\sqrt {-4\,{x}^{4}+{{\it \_f}}^{2}}+40\, \int _{{\it \_b}}^{x}\!{\frac {{{\it \_a}}^{3}}{ \left ( \sqrt {-4\,{{ \it \_a}}^{4}+{{\it \_f}}^{2}}+5\,{\it \_f} \right ) ^{2}\sqrt {-4\,{{ \it \_a}}^{4}+{{\it \_f}}^{2}}}}\,{\rm d}{\it \_a}{\it \_f}-1 \right ) }{d{\it \_f}}+{\it \_C1}=0,\int _{{\it \_b}}^{x}\!-{\frac {1}{{\it \_a} } \left ( -y \left ( x \right ) +\sqrt {-4\,{{\it \_a}}^{4}+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( -5\,y \left ( x \right ) +\sqrt {-4\,{{\it \_a}}^{4}+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!-2\,{\frac {1}{-5\,{\it \_f}+\sqrt {-4\,{x}^{4}+{{\it \_f} }^{2}}} \left ( 8\,\int _{{\it \_b}}^{x}\!{\frac {{{\it \_a}}^{3}}{ \left ( -5\,{\it \_f}+\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}} \right ) ^{2}\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f}}^{2}}}}\,{\rm d}{ \it \_a}\sqrt {-4\,{x}^{4}+{{\it \_f}}^{2}}-40\,\int _{{\it \_b}}^{x}\! {\frac {{{\it \_a}}^{3}}{ \left ( -5\,{\it \_f}+\sqrt {-4\,{{\it \_a}}^ {4}+{{\it \_f}}^{2}} \right ) ^{2}\sqrt {-4\,{{\it \_a}}^{4}+{{\it \_f} }^{2}}}}\,{\rm d}{\it \_a}{\it \_f}-1 \right ) }{d{\it \_f}}+{\it \_C1} =0 \right \} \]