3.473   ODE No. 473

$$\boxed{{\displaystyle (y\left(x\right)-2x){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-2(x-1)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+y\left(x\right)-2=0}}$$

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

Mathematica: cpu = 0.407052 (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 = 0.936 (sec), leaf count = 78 $$\{y\left(x\right)=2+\mathit{\_}\mathit{C}\mathit{1}-\sqrt{-{\mathit{\_}\mathit{C}\mathit{1}}^2+2\mathit{\_}\mathit{C}\mathit{1}(x-1)},y\left(x\right)=2+\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}-\frac{1}{2}\sqrt{-{\mathit{\_}\mathit{C}\mathit{1}}^2+4\mathit{\_}\mathit{C}\mathit{1}(x-1)},y\left(x\right)=-\sqrt{2}x+\sqrt{2}+x+1,y\left(x\right)=\sqrt{2}x-\sqrt{2}+x+1\}$$