\[ \boxed { \left ( 2\,y \left ( x \right ) -4\,x+1 \right ) ^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) -2\,x \right ) ^{2}=0} \]
Mathematica: cpu = 0.912616 (sec), leaf count = 77 \[ \text {Solve}\left [\frac {y(x)}{2}+\frac {1}{196} \left (14 y(x)-\left (8-9 \sqrt {2}\right ) \log \left (-7 y(x)+14 x+\sqrt {2}-4\right )-\left (8+9 \sqrt {2}\right ) \log \left (7 y(x)-14 x+\sqrt {2}+4\right )-28 x\right )=c_1,y(x)\right ] \]
Maple: cpu = 0.063 (sec), leaf count = 56 \[ \left \{ -{\frac {x}{7}}+{\frac {4\,y \left ( x \right ) }{7}}-{\frac {2 \,\ln \left ( 7\, \left ( y \left ( x \right ) -2\,x \right ) ^{2}+8\,y \left ( x \right ) -16\,x+2 \right ) }{49}}-{\frac {9\,\sqrt {2}}{98}{ \it Artanh} \left ( {\frac { \left ( 14\,y \left ( x \right ) -28\,x+8 \right ) \sqrt {2}}{4}} \right ) }-{\it \_C1}=0 \right \} \]