2.515   ODE No. 515

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

$$f(x^2+y(x{)}^2)(y^{\prime }(x{)}^2+1)-{(x{y}^{\prime }(x)-y(x))}^2=0$$ ✗ Mathematica : cpu = 300. (sec), leaf count = 0 , timed out

$Aborted

✓ Maple : cpu = 2.196 (sec), leaf count = 113

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