3.496   ODE No. 496

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

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

Mathematica: cpu = 95.092075 (sec), leaf count = 65 $$\{\{y(x)\to c_1-\sqrt{a^2+2c_{1}x-c_1^2-x^2}\},\{y(x)\to \sqrt{a^2+2c_{1}x-c_1^2-x^2}+c_1\}\}$$

Maple: cpu = 0.718 (sec), leaf count = 130 $$\{y\left(x\right)=x-\sqrt{2}a,y\left(x\right)=x+\sqrt{2}a,y\left(x\right)=x+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+{\int }^{\mathit{\_}\mathit{Z}}-\frac{1}{2{\mathit{\_}\mathit{a}}^2-4a^2}({\mathit{\_}\mathit{a}}^2-2a^2+\sqrt{-{\mathit{\_}\mathit{a}}^2({\mathit{\_}\mathit{a}}^2-2a^2)})d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}),y\left(x\right)=x+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{2{\mathit{\_}\mathit{a}}^2-4a^2}(2a^2-{\mathit{\_}\mathit{a}}^2+\sqrt{-{\mathit{\_}\mathit{a}}^2({\mathit{\_}\mathit{a}}^2-2a^2)})d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})\}$$