\[ (y(x)-2 x) y'(x)^2-2 (x-1) y'(x)+y(x)-2=0 \] ✓ Mathematica : cpu = 0.307533 (sec), leaf count = 165
\[\left \{\left \{y(x)\to \frac {1}{2} \left (-\sqrt {-4 e^{c_1} x+4 e^{c_1}-e^{2 c_1}}+4-e^{c_1}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\sqrt {-4 e^{c_1} x+4 e^{c_1}-e^{2 c_1}}+4-e^{c_1}\right )\right \},\left \{y(x)\to -\sqrt {-2 e^{c_1} x+2 e^{c_1}-e^{2 c_1}}+2-e^{c_1}\right \},\left \{y(x)\to \sqrt {-2 e^{c_1} x+2 e^{c_1}-e^{2 c_1}}+2-e^{c_1}\right \}\right \}\] ✓ Maple : cpu = 0.706 (sec), leaf count = 71
\[y \relax (x ) = -\sqrt {2}\, x +\sqrt {2}+x +1\]