\[ y'(x)=\frac {x^6-3 x^4 y(x)+2 x^3+3 x^2 y(x)^2-2 x y(x)-y(x)^3-2 x}{x^2-y(x)-1} \] ✓ Mathematica : cpu = 0.153651 (sec), leaf count = 49
DSolve[Derivative[1][y][x] == (-2*x + 2*x^3 + x^6 - 2*x*y[x] - 3*x^4*y[x] + 3*x^2*y[x]^2 - y[x]^3)/(-1 + x^2 - y[x]),y[x],x]
\[\left \{\left \{y(x)\to x^2+\frac {1}{1-\frac {1}{\sqrt {-2 x+c_1}}}-1\right \},\left \{y(x)\to x^2+\frac {1}{1+\frac {1}{\sqrt {-2 x+c_1}}}-1\right \}\right \}\] ✓ Maple : cpu = 0.039 (sec), leaf count = 73
dsolve(diff(y(x),x) = (-2*x*y(x)+2*x^3-2*x-y(x)^3+3*x^2*y(x)^2-3*y(x)*x^4+x^6)/(-y(x)+x^2-1),y(x))
\[y \left (x \right ) = \frac {-2 c_{1} x^{2}+2 x^{3}+\sqrt {2 c_{1}-2 x +1}-1}{-2 c_{1}+2 x}\]