\[ y'(x)=\frac {x^6-3 x^4 y(x)^2+x^3+3 x^2 y(x)^4-x y(x)^2-y(x)^6-x}{y(x) \left (x^2-y(x)^2-1\right )} \] ✓ Mathematica : cpu = 0.156145 (sec), leaf count = 295
DSolve[Derivative[1][y][x] == (-x + x^3 + x^6 - x*y[x]^2 - 3*x^4*y[x]^2 + 3*x^2*y[x]^4 - y[x]^6)/(y[x]*(-1 + x^2 - y[x]^2)),y[x],x]
\[\left \{\left \{y(x)\to -\frac {1}{2} \sqrt {\frac {4 x^3}{x-c_1}-\frac {4 c_1 x^2}{x-c_1}-\frac {\sqrt {-4 x+1+4 c_1}}{x-c_1}-\frac {1}{x-c_1}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {\frac {4 x^3}{x-c_1}-\frac {4 c_1 x^2}{x-c_1}-\frac {\sqrt {-4 x+1+4 c_1}}{x-c_1}-\frac {1}{x-c_1}}\right \},\left \{y(x)\to -\frac {1}{2} \sqrt {\frac {4 x^3}{x-c_1}-\frac {4 c_1 x^2}{x-c_1}+\frac {\sqrt {-4 x+1+4 c_1}}{x-c_1}-\frac {1}{x-c_1}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {\frac {4 x^3}{x-c_1}-\frac {4 c_1 x^2}{x-c_1}+\frac {\sqrt {-4 x+1+4 c_1}}{x-c_1}-\frac {1}{x-c_1}}\right \}\right \}\] ✓ Maple : cpu = 0.201 (sec), leaf count = 177
dsolve(diff(y(x),x) = (-x*y(x)^2+x^3-x-y(x)^6+3*y(x)^4*x^2-3*y(x)^2*x^4+x^6)/(-y(x)^2+x^2-1)/y(x),y(x))
\[y \left (x \right ) = \frac {\sqrt {\left (-x +c_{1}\right ) \left (4 x^{2} c_{1}-4 x^{3}+\sqrt {4 c_{1}-4 x +1}+1\right )}}{2 x -2 c_{1}}\]