2.1784   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 = 0.260216 (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 = 1.007 (sec), leaf count = 49

$$\{y\left(x\right)=\frac{1}{{\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{2}}(\mathit{\_}\mathit{C}\mathit{1}+1)}(i{\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{2}}x(\mathit{\_}\mathit{C}\mathit{1}+1)-{\left((2i\mathit{\_}\mathit{C}\mathit{1}+2i-{\mathrm{e}}^{\mathit{\_}\mathit{Z}})x\right)}^{{\mathit{\_}\mathit{C}\mathit{1}}^{-1}}{\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}}{\mathit{\_}\mathit{C}\mathit{1}}})\}$$