\[ \boxed { \left ( y \left ( x \right ) -2\,x \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-2\, \left ( x-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) -2=0} \]
Mathematica: cpu = 0.407052 (sec), leaf count = 165 \[ \left \{\left \{y(x)\to \frac {1}{2} \left (-\sqrt {-4 e^{c_1} x+4 e^{c_1}-e^{2 c_1}}-e^{c_1}+4\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\sqrt {-4 e^{c_1} x+4 e^{c_1}-e^{2 c_1}}-e^{c_1}+4\right )\right \},\left \{y(x)\to -\sqrt {-2 e^{c_1} x+2 e^{c_1}-e^{2 c_1}}-e^{c_1}+2\right \},\left \{y(x)\to \sqrt {-2 e^{c_1} x+2 e^{c_1}-e^{2 c_1}}-e^{c_1}+2\right \}\right \} \]
Maple: cpu = 0.936 (sec), leaf count = 78 \[ \left \{ y \left ( x \right ) =2+{\it \_C1}-\sqrt {-{{\it \_C1}}^{2}+2\, {\it \_C1}\, \left ( x-1 \right ) },y \left ( x \right ) =2+{\frac {{\it \_C1}}{2}}-{\frac {1}{2}\sqrt {-{{\it \_C1}}^{2}+4\,{\it \_C1}\, \left ( x-1 \right ) }},y \left ( x \right ) =-\sqrt {2}x+\sqrt {2}+x+1,y \left ( x \right ) =\sqrt {2}x-\sqrt {2}+x+1 \right \} \]