\[ \boxed { \left ( \left ( y \left ( x \right ) \right ) ^{3}-{x}^{3} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -{x}^{2}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.051007 (sec), leaf count = 201 \[ \left \{\left \{y(x)\to \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to -\sqrt [3]{-1} \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to (-1)^{2/3} \sqrt [3]{x^3-\sqrt {x^6-e^{6 c_1}}}\right \},\left \{y(x)\to \sqrt [3]{\sqrt {x^6-e^{6 c_1}}+x^3}\right \},\left \{y(x)\to -\sqrt [3]{-1} \sqrt [3]{\sqrt {x^6-e^{6 c_1}}+x^3}\right \},\left \{y(x)\to (-1)^{2/3} \sqrt [3]{\sqrt {x^6-e^{6 c_1}}+x^3}\right \}\right \} \]
Maple: cpu = 0.250 (sec), leaf count = 391 \[ \left \{ y \left ( x \right ) ={x{\frac {1}{\sqrt [3]{- \left ( {x}^{3}{ \it \_C1}-\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}} }}},y \left ( x \right ) ={x{\frac {1}{\sqrt [3]{- \left ( {x}^{3}{\it \_C1}+\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}}}, y \left ( x \right ) ={\frac {x}{ \left ( -{\frac {1}{2}}-{\frac {i}{2}} \sqrt {3} \right ) ^{2}}{\frac {1}{\sqrt [3]{- \left ( {x}^{3}{\it \_C1} -\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}}},y \left ( x \right ) ={\frac {x}{ \left ( -{\frac {1}{2}}-{\frac {i}{2}} \sqrt {3} \right ) ^{2}}{\frac {1}{\sqrt [3]{- \left ( {x}^{3}{\it \_C1} +\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}}},y \left ( x \right ) ={\frac {x}{ \left ( -{\frac {1}{2}}+{\frac {i}{2}} \sqrt {3} \right ) ^{2}}{\frac {1}{\sqrt [3]{- \left ( {x}^{3}{\it \_C1} -\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}}},y \left ( x \right ) ={\frac {x}{ \left ( -{\frac {1}{2}}+{\frac {i}{2}} \sqrt {3} \right ) ^{2}}{\frac {1}{\sqrt [3]{- \left ( {x}^{3}{\it \_C1} +\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}}},y \left ( x \right ) ={\frac {x}{ \left ( {\frac {1}{2}}-{\frac {i}{2}} \sqrt {3} \right ) ^{2}}{\frac {1}{\sqrt [3]{- \left ( {x}^{3}{\it \_C1} -\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}}},y \left ( x \right ) ={\frac {x}{ \left ( {\frac {1}{2}}-{\frac {i}{2}} \sqrt {3} \right ) ^{2}}{\frac {1}{\sqrt [3]{- \left ( {x}^{3}{\it \_C1} +\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}}},y \left ( x \right ) ={\frac {x}{ \left ( {\frac {1}{2}}+{\frac {i}{2}} \sqrt {3} \right ) ^{2}}{\frac {1}{\sqrt [3]{- \left ( {x}^{3}{\it \_C1} -\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}}},y \left ( x \right ) ={\frac {x}{ \left ( {\frac {1}{2}}+{\frac {i}{2}} \sqrt {3} \right ) ^{2}}{\frac {1}{\sqrt [3]{- \left ( {x}^{3}{\it \_C1} +\sqrt {{{\it \_C1}}^{2}{x}^{6}+1} \right ) {x}^{3}{\it \_C1}}}}} \right \} \]