#### 2.487   ODE No. 487

$-6 x^3 y'(x)+4 x^2 y(x)+y(x)^2 y'(x)^2=0$ Mathematica : cpu = 0.285889 (sec), leaf count = 157

$\left \{\text {Solve}\left [\frac {3}{4} \log (y(x))-\frac {\sqrt {9 x^6-4 x^2 y(x)^3} \tanh ^{-1}\left (\frac {3 x^2}{\sqrt {9 x^4-4 y(x)^3}}\right )}{2 x \sqrt {9 x^4-4 y(x)^3}}=c_1,y(x)\right ],\text {Solve}\left [\frac {\sqrt {9 x^6-4 x^2 y(x)^3} \tanh ^{-1}\left (\frac {3 x^2}{\sqrt {9 x^4-4 y(x)^3}}\right )}{2 x \sqrt {9 x^4-4 y(x)^3}}+\frac {3}{4} \log (y(x))=c_1,y(x)\right ]\right \}$ Maple : cpu = 0.548 (sec), leaf count = 100

$\left \{ y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!-{\frac {3}{4\,{\it \_a}\, \left ( 4\,{{\it \_a}}^{3}-9 \right ) } \left ( 4\,{{\it \_a}}^{3}+3\,\sqrt {-4\,{{\it \_a}}^{3}+9}-9 \right ) }{d{\it \_a}}+{\it \_C1} \right ) {x}^{{\frac {4}{3}}},y \left ( x \right ) ={\frac {\sqrt [3]{18}}{2}{x}^{{\frac {4}{3}}}},y \left ( x \right ) =-{\frac {\sqrt [3]{18} \left ( 1+i\sqrt {3} \right ) }{4}{x}^{{\frac {4}{3}}}},y \left ( x \right ) ={\frac {\sqrt [3]{18} \left ( i\sqrt {3}-1 \right ) }{4}{x}^{{\frac {4}{3}}}} \right \}$