\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-x \left ( y \left ( x \right ) \right ) ^{2}+{x}^{3}-x- \left ( y \left ( x \right ) \right ) ^{6}+3\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{4}-3\,{x}^{4} \left ( y \left ( x \right ) \right ) ^{2}+{x}^{6}}{ \left ( - \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}-1 \right ) y \left ( x \right ) }}=0} \]
Mathematica: cpu = 0.109514 (sec), leaf count = 295 \[ \left \{\left \{y(x)\to -\frac {1}{2} \sqrt {\frac {4 x^3}{x-c_1}-\frac {4 c_1 x^2}{x-c_1}-\frac {\sqrt {4 c_1-4 x+1}}{x-c_1}-\frac {1}{x-c_1}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {\frac {4 x^3}{x-c_1}-\frac {4 c_1 x^2}{x-c_1}-\frac {\sqrt {4 c_1-4 x+1}}{x-c_1}-\frac {1}{x-c_1}}\right \},\left \{y(x)\to -\frac {1}{2} \sqrt {\frac {4 x^3}{x-c_1}-\frac {4 c_1 x^2}{x-c_1}+\frac {\sqrt {4 c_1-4 x+1}}{x-c_1}-\frac {1}{x-c_1}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {\frac {4 x^3}{x-c_1}-\frac {4 c_1 x^2}{x-c_1}+\frac {\sqrt {4 c_1-4 x+1}}{x-c_1}-\frac {1}{x-c_1}}\right \}\right \} \]
Maple: cpu = 0.171 (sec), leaf count = 175 \[ \left \{ y \left ( x \right ) =-{\frac {1}{2\,{\it \_C1}+6\,x}\sqrt { \left ( {\it \_C1}+3\,x \right ) \left ( 4\,{\it \_C1}\,{x}^{2}+12\,{x} ^{3}+\sqrt {-12\,{\it \_C1}-36\,x+9}-3 \right ) }},y \left ( x \right ) = {\frac {1}{2\,{\it \_C1}+6\,x}\sqrt { \left ( {\it \_C1}+3\,x \right ) \left ( 4\,{\it \_C1}\,{x}^{2}+12\,{x}^{3}+\sqrt {-12\,{\it \_C1}-36\, x+9}-3 \right ) }},y \left ( x \right ) =-{\frac {1}{2\,{\it \_C1}+6\,x} \sqrt {- \left ( {\it \_C1}+3\,x \right ) \left ( -4\,{\it \_C1}\,{x}^{2 }-12\,{x}^{3}+\sqrt {-12\,{\it \_C1}-36\,x+9}+3 \right ) }},y \left ( x \right ) ={\frac {1}{2\,{\it \_C1}+6\,x}\sqrt {- \left ( {\it \_C1}+3\, x \right ) \left ( -4\,{\it \_C1}\,{x}^{2}-12\,{x}^{3}+\sqrt {-12\,{ \it \_C1}-36\,x+9}+3 \right ) }} \right \} \]