2.473   ODE No. 473

1. Problem in Latex
2. Mathematica input
3. Maple input

$$(y(x)-2x)y^{\prime }(x{)}^2-2(x-1)y^{\prime }(x)+y(x)-2=0$$ ✓ Mathematica : cpu = 0.266758 (sec), leaf count = 165

$$\{\{y(x)\to \frac{1}{2}(-\sqrt{-4e^{c_1}x+4e^{c_1}-e^{2c_1}}-e^{c_1}+4)\},\{y(x)\to \frac{1}{2}(\sqrt{-4e^{c_1}x+4e^{c_1}-e^{2c_1}}-e^{c_1}+4)\},\{y(x)\to -\sqrt{-2e^{c_1}x+2e^{c_1}-e^{2c_1}}-e^{c_1}+2\},\{y(x)\to \sqrt{-2e^{c_1}x+2e^{c_1}-e^{2c_1}}-e^{c_1}+2\}\}$$ ✓ Maple : cpu = 1.901 (sec), leaf count = 71

$$\{y\left(x\right)=2+\mathit{\_}\mathit{C}\mathit{1}-\sqrt{\mathit{\_}\mathit{C}\mathit{1}(-\mathit{\_}\mathit{C}\mathit{1}+2x-2)},y\left(x\right)=2+\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}-\frac{1}{2}\sqrt{\mathit{\_}\mathit{C}\mathit{1}(-\mathit{\_}\mathit{C}\mathit{1}+4x-4)},y\left(x\right)=(x-1)\sqrt{2}+x+1,y\left(x\right)=-\sqrt{2}x+\sqrt{2}+x+1\}$$