3.515   ODE No. 515

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

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

Mathematica: cpu = 0 (sec), leaf count = 0 $$\text{Hanged}$$

Maple: cpu = 1.888 (sec), leaf count = 113 $$\{y\left(x\right)=x{(\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\mathit{\_}\mathit{Z}+{\int }^{\frac{x^2({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+1)}{{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2}}-\frac{1}{2\mathit{\_}\mathit{a}(f\left(\mathit{\_}\mathit{a}\right)-\mathit{\_}\mathit{a})}\sqrt{-(f\left(\mathit{\_}\mathit{a}\right)-\mathit{\_}\mathit{a})f\left(\mathit{\_}\mathit{a}\right)}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})\right))}^{-1},y\left(x\right)=x{(\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\mathit{\_}\mathit{Z}+{\int }^{\frac{x^2({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+1)}{{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2}}\frac{1}{2\mathit{\_}\mathit{a}(f\left(\mathit{\_}\mathit{a}\right)-\mathit{\_}\mathit{a})}\sqrt{-(f\left(\mathit{\_}\mathit{a}\right)-\mathit{\_}\mathit{a})f\left(\mathit{\_}\mathit{a}\right)}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})\right))}^{-1}\}$$