\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {3\,{x}^{3}+\sqrt {-9\,{x}^{4}+4\, \left ( y \left ( x \right ) \right ) ^{3}}+{x}^{2}\sqrt {-9\,{x}^{4}+4\, \left ( y \left ( x \right ) \right ) ^{3}}+{x}^{3}\sqrt {-9\,{x}^{4}+4\, \left ( y \left ( x \right ) \right ) ^{3}}}{ \left ( y \left ( x \right ) \right ) ^{2}}}=0} \]
Mathematica: cpu = 4.914124 (sec), leaf count = 227 \[ \left \{\left \{y(x)\to -\frac {1}{2} \sqrt [3]{-\frac {1}{2}} \sqrt [3]{72 c_1 x^4+96 c_1 x^3+288 c_1 x+144 c_1^2+9 x^8+24 x^7+16 x^6+72 x^5+132 x^4+144 x^2}\right \},\left \{y(x)\to \frac {\sqrt [3]{72 c_1 x^4+96 c_1 x^3+288 c_1 x+144 c_1^2+9 x^8+24 x^7+16 x^6+72 x^5+132 x^4+144 x^2}}{2 \sqrt [3]{2}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} \sqrt [3]{72 c_1 x^4+96 c_1 x^3+288 c_1 x+144 c_1^2+9 x^8+24 x^7+16 x^6+72 x^5+132 x^4+144 x^2}}{2 \sqrt [3]{2}}\right \}\right \} \]
Maple: cpu = 0.187 (sec), leaf count = 44 \[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{ \frac {1}{\sqrt {-9\,{x}^{4}+4\,{{\it \_a}}^{3}}}}}\,{\rm d}{\it \_a}- {\frac {{x}^{4}}{4}}-{\frac {{x}^{3}}{3}}-x-{\it \_C1}=0 \right \} \]