#### 2.537   ODE No. 537

$x^3 y'(x)^3-3 x^2 y(x) y'(x)^2+\left (x^6+3 x y(x)^2\right ) y'(x)-2 x^5 y(x)-y(x)^3=0$ Mathematica : cpu = 300.004 (sec), leaf count = 0 , timed out

\$Aborted

Maple : cpu = 5.886 (sec), leaf count = 250

$\left \{ y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!{\frac {2}{3\,{\it \_a}\, \left ( 27\,{{\it \_a}}^{2}+4 \right ) } \left ( 27\, \left ( -4\,{\frac {-9\,{\it \_a}+\sqrt {81\,{{\it \_a}}^{2}+12}}{ \left ( 27\,{{\it \_a}}^{2}+4 \right ) \sqrt {81\,{{\it \_a}}^{2}+12}}} \right ) ^{2/3}{{\it \_a}}^{2}-27\,{{\it \_a}}^{2}\sqrt [3]{-4\,{\frac {-9\,{\it \_a}+\sqrt {81\,{{\it \_a}}^{2}+12}}{ \left ( 27\,{{\it \_a}}^{2}+4 \right ) \sqrt {81\,{{\it \_a}}^{2}+12}}}}+4\, \left ( -4\,{\frac {-9\,{\it \_a}+\sqrt {81\,{{\it \_a}}^{2}+12}}{ \left ( 27\,{{\it \_a}}^{2}+4 \right ) \sqrt {81\,{{\it \_a}}^{2}+12}}} \right ) ^{2/3}-4\,\sqrt [3]{-4\,{\frac {-9\,{\it \_a}+\sqrt {81\,{{\it \_a}}^{2}+12}}{ \left ( 27\,{{\it \_a}}^{2}+4 \right ) \sqrt {81\,{{\it \_a}}^{2}+12}}}}+4 \right ) {\frac {1}{\sqrt [3]{-4\,{\frac {-9\,{\it \_a}+\sqrt {81\,{{\it \_a}}^{2}+12}}{ \left ( 27\,{{\it \_a}}^{2}+4 \right ) \sqrt {81\,{{\it \_a}}^{2}+12}}}}}}}{d{\it \_a}}+{\it \_C1} \right ) {x}^{{\frac {5}{2}}},y \left ( x \right ) =-{\frac {2\,{x}^{2}}{9}\sqrt {-3\,x}},y \left ( x \right ) ={\frac {2\,{x}^{2}}{9}\sqrt {-3\,x}} \right \}$