8.194   ODE No. 1784

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

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

Mathematica: cpu = 0.264034 (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 = 2.324 (sec), leaf count = 52 $$\{y\left(x\right)=\frac{x(i\mathit{\_}\mathit{C}\mathit{1}+i-{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\ln \left(x\right)\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{Z}\mathit{\_}\mathit{C}\mathit{1}-\ln \left((2i\mathit{\_}\mathit{C}\mathit{1}+2i-{\mathrm{e}}^{\mathit{\_}\mathit{Z}})x\right)-\mathit{\_}\mathit{C}\mathit{2})})}{\mathit{\_}\mathit{C}\mathit{1}+1}\}$$