\[ -\left (-a+x^3+y(x)^3\right ) y'(x)+x^2 y(x)+x y(x)^2 y'(x)^2=0 \] ✓ Mathematica : cpu = 0.0746197 (sec), leaf count = 36
\[\left \{y(x)\to \frac {\sqrt [3]{c_1} \sqrt [3]{a-x^3+c_1 x^3}}{\sqrt [3]{-1+c_1}}\right \}\] ✓ Maple : cpu = 0.822 (sec), leaf count = 247
\[\left \{-c_{1}+\int _{\textit {\_b}}^{y \left (x \right )}\frac {\textit {\_a}^{2}}{\sqrt {x^{6}+\left (-2 \textit {\_a}^{3}-2 a \right ) x^{3}+\left (-\textit {\_a}^{3}+a \right )^{2}}}d \textit {\_a} -\frac {\ln \left (x \right )}{2} = 0, -c_{1}+\int _{\textit {\_b}}^{y \left (x \right )}\frac {\textit {\_a}^{2}}{\sqrt {x^{6}+\left (-2 \textit {\_a}^{3}-2 a \right ) x^{3}+\left (-\textit {\_a}^{3}+a \right )^{2}}}d \textit {\_a} +\frac {\ln \left (x \right )}{2} = 0, y \left (x \right ) = \left (x^{3}+a -2 \sqrt {a x}\, x \right )^{\frac {1}{3}}, y \left (x \right ) = \left (x^{3}+a +2 \sqrt {a x}\, x \right )^{\frac {1}{3}}, y \left (x \right ) = -\frac {\left (x^{3}+a -2 \sqrt {a x}\, x \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2}, y \left (x \right ) = \frac {\left (x^{3}+a -2 \sqrt {a x}\, x \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2}, y \left (x \right ) = -\frac {\left (x^{3}+a +2 \sqrt {a x}\, x \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2}, y \left (x \right ) = \frac {\left (x^{3}+a +2 \sqrt {a x}\, x \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2}\right \}\]