\[ \boxed { x \left ( y \left ( x \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}- \left ( \left ( y \left ( x \right ) \right ) ^{3}+{x}^{3}-a \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +{x}^{2}y \left ( x \right ) =0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 1.201 (sec), leaf count = 303 \[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{ \frac {1}{\sqrt {{{\it \_a}}^{6}+ \left ( -2\,{x}^{3}-2\,a \right ) {{ \it \_a}}^{3}+ \left ( -{x}^{3}+a \right ) ^{2}}}}}\,{\rm d}{\it \_a}-{ \frac {\ln \left ( x \right ) }{2}}-{\it \_C1}=0,\int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{\frac {1}{\sqrt {{{\it \_a}}^{6} + \left ( -2\,{x}^{3}-2\,a \right ) {{\it \_a}}^{3}+ \left ( -{x}^{3}+a \right ) ^{2}}}}}\,{\rm d}{\it \_a}+{\frac {\ln \left ( x \right ) }{2} }-{\it \_C1}=0,y \left ( x \right ) =\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}} ,y \left ( x \right ) =\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}},y \left ( x \right ) =-{\frac {1}{2}\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}}}-{\frac {i }{2}}\sqrt {3}\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}},y \left ( x \right ) = -{\frac {1}{2}\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}}}+{\frac {i}{2}} \sqrt {3}\sqrt [3]{{x}^{3}+a-2\,x\sqrt {ax}},y \left ( x \right ) =-{ \frac {1}{2}\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}}}-{\frac {i}{2}}\sqrt { 3}\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}},y \left ( x \right ) =-{\frac {1}{ 2}\sqrt [3]{{x}^{3}+a+2\,x\sqrt {ax}}}+{\frac {i}{2}}\sqrt {3}\sqrt [3 ]{{x}^{3}+a+2\,x\sqrt {ax}} \right \} \]