8.89   ODE No. 1679

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

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

Mathematica: cpu = 0.042005 (sec), leaf count = 33 $$\left\{\{y(x)\to -x\cot \left(c_1\right)+{\csc }^2\left(c_1\right)\log (-x\sin \left(c_1\right)-\cos \left(c_1\right))+c_2\}\right\}$$

Maple: cpu = 0.826 (sec), leaf count = 27 $$\{y\left(x\right)=\frac{x}{\mathit{\_}\mathit{C}\mathit{1}}+\ln (x\mathit{\_}\mathit{C}\mathit{1}-1)+\frac{\ln (x\mathit{\_}\mathit{C}\mathit{1}-1)}{{\mathit{\_}\mathit{C}\mathit{1}}^2}+\mathit{\_}\mathit{C}\mathit{2}\}$$