2.487   ODE No. 487

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

\[ -6 x^3 y'(x)+4 x^2 y(x)+y(x)^2 y'(x)^2=0 \] Mathematica : cpu = 299.998 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 0.433 (sec), leaf count = 114

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