\[ -\left (-a+x^3+y(x)^3\right ) y'(x)+x^2 y(x)+x y(x)^2 y'(x)^2=0 \] ✓ Mathematica : cpu = 0.332354 (sec), leaf count = 51
\[\left \{y(x)\to -\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{2 c_1+1} \sqrt [3]{2 a c_1-a+2 x^3}}{\sqrt [3]{2 c_1-1}}\right \}\] ✓ Maple : cpu = 1.107 (sec), leaf count = 247
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{\frac {1}{\sqrt {{x}^{6}+ \left ( -2\,{{\it \_a}}^{3}-2\,a \right ) {x}^{3}+ \left ( -{{\it \_a}}^{3}+a \right ) ^{2}}}}}\,{\rm d}{\it \_a}-{\frac {\ln \left ( x \right ) }{2}}-{\it \_C1}=0,\int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{\frac {1}{\sqrt {{x}^{6}+ \left ( -2\,{{\it \_a}}^{3}-2\,a \right ) {x}^{3}+ \left ( -{{\it \_a}}^{3}+a \right ) ^{2}}}}}\,{\rm d}{\it \_a}+{\frac {\ln \left ( x \right ) }{2}}-{\it \_C1}=0,y \left ( x \right ) =\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}},y \left ( x \right ) =\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}},y \left ( x \right ) =-{\frac {1+i\sqrt {3}}{2}\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}}},y \left ( x \right ) ={\frac {i\sqrt {3}-1}{2}\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}}},y \left ( x \right ) =-{\frac {1+i\sqrt {3}}{2}\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}}},y \left ( x \right ) ={\frac {i\sqrt {3}-1}{2}\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}}} \right \} \]