3.487   ODE No. 487

\[ \boxed { \left ( y \left ( x \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-6\,{x}^{3}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +4\,{x}^{2}y \left ( x \right ) =0} \]

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

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

Maple: cpu = 0.858 (sec), leaf count = 114 \[ \left \{ y \left ( x \right ) = \left ( -{\frac {\sqrt [3]{18}}{4}\sqrt [ 3]{x}}-{\frac {i}{4}}\sqrt {3}\sqrt [3]{18}\sqrt [3]{x} \right ) x,y \left ( x \right ) = \left ( -{\frac {\sqrt [3]{18}}{4}\sqrt [3]{x}}+{ \frac {i}{4}}\sqrt {3}\sqrt [3]{18}\sqrt [3]{x} \right ) x,y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z} }\!-{\frac {3}{4\,{\it \_a}\, \left ( 4\,{{\it \_a}}^{3}-9 \right ) } \left ( 4\,{{\it \_a}}^{3}+3\,\sqrt {-4\,{{\it \_a}}^{3}+9}-9 \right ) }{d{\it \_a}}+{\it \_C1} \right ) {x}^{{\frac {4}{3}}},y \left ( x \right ) ={\frac {\sqrt [3]{18}}{2}{x}^{{\frac {4}{3}}}} \right \} \]