\[ -\left (-a+x^3+y(x)^3\right ) y'(x)+x^2 y(x)+x y(x)^2 y'(x)^2=0 \] ✗ Mathematica : cpu = 299.998 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.81 (sec), leaf count = 303
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{\frac {1}{\sqrt {{{\it \_a}}^{6}+ \left ( -2\,{x}^{3}-2\,a \right ) {{\it \_a}}^{3}+ \left ( -{x}^{3}+a \right ) ^{2}}}}}\,{\rm d}{\it \_a}-{\frac {\ln \left ( x \right ) }{2}}-{\it \_C1}=0,\int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{\frac {1}{\sqrt {{{\it \_a}}^{6}+ \left ( -2\,{x}^{3}-2\,a \right ) {{\it \_a}}^{3}+ \left ( -{x}^{3}+a \right ) ^{2}}}}}\,{\rm d}{\it \_a}+{\frac {\ln \left ( x \right ) }{2}}-{\it \_C1}=0,y \left ( x \right ) =\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}},y \left ( x \right ) =\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}},y \left ( x \right ) =-{\frac {1}{2}\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}}}-{\frac {i}{2}}\sqrt {3}\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}},y \left ( x \right ) =-{\frac {1}{2}\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}}}+{\frac {i}{2}}\sqrt {3}\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}},y \left ( x \right ) =-{\frac {1}{2}\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}}}-{\frac {i}{2}}\sqrt {3}\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}},y \left ( x \right ) =-{\frac {1}{2}\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}}}+{\frac {i}{2}}\sqrt {3}\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}} \right \} \]