2.496   ODE No. 496

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

$$(y(x)-x{)}^2(y^{\prime }(x{)}^2+1)-a^2{(y^{\prime }(x)+1)}^2=0$$ ✓ Mathematica : cpu = 18.3183 (sec), leaf count = 17831 $$\text{Too large to display}$$ ✓ Maple : cpu = 0.473 (sec), leaf count = 130

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