8.195   ODE No. 1785

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

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

Mathematica: cpu = 0.363546 (sec), leaf count = 95 $$\{\{y(x)\to \frac{1}{2}(-\sqrt{4x(e^{c_2}-x)+e^{2c_2}{\cot }^2\left(c_1\right)}-e^{c_2}\cot \left(c_1\right))\},\{y(x)\to \frac{1}{2}(\sqrt{4x(e^{c_2}-x)+e^{2c_2}{\cot }^2\left(c_1\right)}-e^{c_2}\cot \left(c_1\right))\}\}$$

Maple: cpu = 1.810 (sec), leaf count = 83 $$\{y\left(x\right)=\frac{1}{4\mathit{\_}\mathit{C}\mathit{2}}(\mathit{\_}\mathit{C}\mathit{1}+1-\sqrt{8i\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{C}\mathit{1}x-16{\mathit{\_}\mathit{C}\mathit{2}}^2{x}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2-8i\mathit{\_}\mathit{C}\mathit{2}x+2\mathit{\_}\mathit{C}\mathit{1}+1}),y\left(x\right)=\frac{1}{4\mathit{\_}\mathit{C}\mathit{2}}(\mathit{\_}\mathit{C}\mathit{1}+1+\sqrt{8i\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{C}\mathit{1}x-16{\mathit{\_}\mathit{C}\mathit{2}}^2{x}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2-8i\mathit{\_}\mathit{C}\mathit{2}x+2\mathit{\_}\mathit{C}\mathit{1}+1})\}$$