\[ \boxed { \left ( 2\, \left ( y \left ( x \right ) \right ) ^{3}+y \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,{x}^{3}-x=0} \]
Mathematica: cpu = 0.011001 (sec), leaf count = 151 \[ \left \{\left \{y(x)\to -\frac {\sqrt {-\sqrt {8 c_1+4 x^4+4 x^2+1}-1}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-\sqrt {8 c_1+4 x^4+4 x^2+1}-1}}{\sqrt {2}}\right \},\left \{y(x)\to -\frac {\sqrt {\sqrt {8 c_1+4 x^4+4 x^2+1}-1}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {\sqrt {8 c_1+4 x^4+4 x^2+1}-1}}{\sqrt {2}}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 113 \[ \left \{ y \left ( x \right ) =-{\frac {1}{2}\sqrt {-2-2\,\sqrt {4\,{x}^ {4}+4\,{x}^{2}+8\,{\it \_C1}+1}}},y \left ( x \right ) ={\frac {1}{2} \sqrt {-2-2\,\sqrt {4\,{x}^{4}+4\,{x}^{2}+8\,{\it \_C1}+1}}},y \left ( x \right ) =-{\frac {1}{2}\sqrt {-2+2\,\sqrt {4\,{x}^{4}+4\,{x}^{2}+8\, {\it \_C1}+1}}},y \left ( x \right ) ={\frac {1}{2}\sqrt {-2+2\,\sqrt {4 \,{x}^{4}+4\,{x}^{2}+8\,{\it \_C1}+1}}} \right \} \]