\[ y'(x)=\frac {x^6-3 x^4 y(x)^2+x^3+3 x^2 y(x)^4-x y(x)^2-y(x)^6-x}{y(x) \left (x^2-y(x)^2-1\right )} \] ✓ Mathematica : cpu = 0.117898 (sec), leaf count = 195
\[\left \{\left \{y(x)\to -\frac {1}{2} \sqrt {-\frac {4 c_1 x^2+\sqrt {4 c_1-4 x+1}-4 x^3+1}{x-c_1}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {-\frac {4 c_1 x^2+\sqrt {4 c_1-4 x+1}-4 x^3+1}{x-c_1}}\right \},\left \{y(x)\to -\frac {1}{2} \sqrt {\frac {-4 c_1 x^2+\sqrt {4 c_1-4 x+1}+4 x^3-1}{x-c_1}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {\frac {-4 c_1 x^2+\sqrt {4 c_1-4 x+1}+4 x^3-1}{x-c_1}}\right \}\right \}\]
✓ Maple : cpu = 0.271 (sec), leaf count = 183
\[ \left \{ y \left ( x \right ) ={\frac {1}{2\,{\it \_C1}+6\,x}\sqrt { \left ( {\it \_C1}+3\,x \right ) \left ( 4\,{\it \_C1}\,{x}^{2}+12\,{x}^{3}-\sqrt {-12\,{\it \_C1}-36\,x+9}-3 \right ) }},y \left ( x \right ) ={\frac {1}{2\,{\it \_C1}+6\,x}\sqrt { \left ( {\it \_C1}+3\,x \right ) \left ( 4\,{\it \_C1}\,{x}^{2}+12\,{x}^{3}+\sqrt {-12\,{\it \_C1}-36\,x+9}-3 \right ) }},y \left ( x \right ) =-{\frac {1}{2\,{\it \_C1}+6\,x}\sqrt { \left ( {\it \_C1}+3\,x \right ) \left ( 4\,{\it \_C1}\,{x}^{2}+12\,{x}^{3}-\sqrt {-12\,{\it \_C1}-36\,x+9}-3 \right ) }},y \left ( x \right ) =-{\frac {1}{2\,{\it \_C1}+6\,x}\sqrt { \left ( {\it \_C1}+3\,x \right ) \left ( 4\,{\it \_C1}\,{x}^{2}+12\,{x}^{3}+\sqrt {-12\,{\it \_C1}-36\,x+9}-3 \right ) }} \right \} \]