\[ (2 y(x)-4 x+1)^2 y'(x)-(y(x)-2 x)^2=0 \] ✓ Mathematica : cpu = 2.58571 (sec), leaf count = 77
DSolve[-(-2*x + y[x])^2 + (1 - 4*x + 2*y[x])^2*Derivative[1][y][x] == 0,y[x],x]
\[\text {Solve}\left [\frac {y(x)}{2}+\frac {1}{196} \left (14 y(x)-\left (8-9 \sqrt {2}\right ) \log \left (-7 y(x)+14 x+\sqrt {2}-4\right )-\left (8+9 \sqrt {2}\right ) \log \left (7 y(x)-14 x+\sqrt {2}+4\right )-28 x\right )=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.066 (sec), leaf count = 56
dsolve((2*y(x)-4*x+1)^2*diff(y(x),x)-(y(x)-2*x)^2 = 0,y(x))
\[-\frac {x}{7}-\frac {9 \sqrt {2}\, \arctanh \left (\frac {\left (7 y \left (x \right )-14 x +4\right ) \sqrt {2}}{2}\right )}{98}-\frac {2 \ln \left (7 \left (y \left (x \right )-2 x \right )^{2}+8 y \left (x \right )-16 x +2\right )}{49}+\frac {4 y \left (x \right )}{7}-c_{1} = 0\]