\[ y'(x)=\frac {-3 x^4 y(x)^2+3 x^2 y(x)^4+x^6+x^3-x y(x)^2-y(x)^6-x}{y(x) \left (x^2-y(x)^2-1\right )} \] ✓ Mathematica : cpu = 0.191283 (sec), leaf count = 295
\[\left \{\left \{y(x)\to -\frac {1}{2} \sqrt {\frac {4 x^3}{x-c_1}-\frac {4 c_1 x^2}{x-c_1}-\frac {\sqrt {-4 x+1+4 c_1}}{x-c_1}-\frac {1}{x-c_1}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {\frac {4 x^3}{x-c_1}-\frac {4 c_1 x^2}{x-c_1}-\frac {\sqrt {-4 x+1+4 c_1}}{x-c_1}-\frac {1}{x-c_1}}\right \},\left \{y(x)\to -\frac {1}{2} \sqrt {\frac {4 x^3}{x-c_1}-\frac {4 c_1 x^2}{x-c_1}+\frac {\sqrt {-4 x+1+4 c_1}}{x-c_1}-\frac {1}{x-c_1}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {\frac {4 x^3}{x-c_1}-\frac {4 c_1 x^2}{x-c_1}+\frac {\sqrt {-4 x+1+4 c_1}}{x-c_1}-\frac {1}{x-c_1}}\right \}\right \}\] ✓ Maple : cpu = 0.394 (sec), leaf count = 183
\[ \left \{ y \left ( x \right ) ={\frac {1}{6\,x+2\,{\it \_C1}}\sqrt { \left ( 3\,x+{\it \_C1} \right ) \left ( 4\,{\it \_C1}\,{x}^{2}+12\,{x}^{3}-\sqrt {-12\,{\it \_C1}-36\,x+9}-3 \right ) }},y \left ( x \right ) ={\frac {1}{6\,x+2\,{\it \_C1}}\sqrt { \left ( 3\,x+{\it \_C1} \right ) \left ( 4\,{\it \_C1}\,{x}^{2}+12\,{x}^{3}+\sqrt {-12\,{\it \_C1}-36\,x+9}-3 \right ) }},y \left ( x \right ) =-{\frac {1}{6\,x+2\,{\it \_C1}}\sqrt { \left ( 3\,x+{\it \_C1} \right ) \left ( 4\,{\it \_C1}\,{x}^{2}+12\,{x}^{3}-\sqrt {-12\,{\it \_C1}-36\,x+9}-3 \right ) }},y \left ( x \right ) =-{\frac {1}{6\,x+2\,{\it \_C1}}\sqrt { \left ( 3\,x+{\it \_C1} \right ) \left ( 4\,{\it \_C1}\,{x}^{2}+12\,{x}^{3}+\sqrt {-12\,{\it \_C1}-36\,x+9}-3 \right ) }} \right \} \]