ODE No. 1784

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

$$(x^2+y(x{)}^2)y^{″}(x)-(x{y}^{\prime }(x)-y(x))(y^{\prime }(x{)}^2+1)=0$$ ✓ Mathematica : cpu = 0.321343 (sec), leaf count = 74

$$\text{Solve}[\frac{1}{2}(i\cot \left(c_1\right)(\log (1-\frac{iy(x)}{x})-\log (1+\frac{iy(x)}{x}))+\log (1-\frac{iy(x)}{x})+\log (1+\frac{iy(x)}{x}))=c_2-\log (x),y(x)]$$ ✓ Maple : cpu = 0.733 (sec), leaf count = 82

$$\{y\left(x\right)=\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\left({\mathrm{e}}^{\frac{i\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}}{-1+\mathit{\_}\mathit{C}\mathit{1}}}\right)}^2{\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{C}\mathit{1}}{-1+\mathit{\_}\mathit{C}\mathit{1}}}\right)}^2{\left(x^{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-1+\mathit{\_}\mathit{C}\mathit{1}}}\right)}^2{\left({\mathrm{e}}^{\frac{i\mathit{\_}\mathit{Z}}{-1+\mathit{\_}\mathit{C}\mathit{1}}}\right)}^2+{\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}}{-1+\mathit{\_}\mathit{C}\mathit{1}}}\right)}^2{\left(x^{{(-1+\mathit{\_}\mathit{C}\mathit{1})}^{-1}}\right)}^2{(\cos \left(\mathit{\_}\mathit{Z}\right))}^2)\right)x\}$$