ODE No. 473

$$(y(x)-2x)y^{\prime }(x{)}^2-2(x-1)y^{\prime }(x)+y(x)-2=0$$ ✓ Mathematica : cpu = 0.307533 (sec), leaf count = 165

DSolve[-2 + y[x] - 2*(-1 + x)*Derivative[1][y][x] + (-2*x + y[x])*Derivative[1][y][x]^2 == 0,y[x],x]
 

$$\{\{y(x)\to \frac{1}{2}(-\sqrt{-4e^{c_1}x+4e^{c_1}-e^{2c_1}}+4-e^{c_1})\},\{y(x)\to \frac{1}{2}(\sqrt{-4e^{c_1}x+4e^{c_1}-e^{2c_1}}+4-e^{c_1})\},\{y(x)\to -\sqrt{-2e^{c_1}x+2e^{c_1}-e^{2c_1}}+2-e^{c_1}\},\{y(x)\to \sqrt{-2e^{c_1}x+2e^{c_1}-e^{2c_1}}+2-e^{c_1}\}\}$$ ✓ Maple : cpu = 0.706 (sec), leaf count = 71

dsolve((y(x)-2*x)*diff(y(x),x)^2-2*(x-1)*diff(y(x),x)+y(x)-2 = 0,y(x))
 

$$y\left(x\right)=-\sqrt{2}x+\sqrt{2}+x+1$$