8.192   ODE No. 1782

$$\boxed{{\displaystyle ({\left(y\left(x\right)\right)}^2+1)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-3y\left(x\right){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2=0}}$$

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

Mathematica: cpu = 0.088011 (sec), leaf count = 93 $$\{\{y(x)\to -\frac{i{c}_1(c_2+x)}{\sqrt{c_1^2{x}^2+2c_2{c}_1^{2}x+c_2^2{c}_1^2-1}}\},\{y(x)\to \frac{i{c}_1(c_2+x)}{\sqrt{c_1^2{x}^2+2c_2{c}_1^{2}x+c_2^2{c}_1^2-1}}\}\}$$

Maple: cpu = 1.638 (sec), leaf count = 56 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x\sqrt{-{({\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+2\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{C}\mathit{2}x+{\mathit{\_}\mathit{C}\mathit{2}}^2-1)}^{-1}}+\mathit{\_}\mathit{C}\mathit{2}\sqrt{-{({\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+2\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{C}\mathit{2}x+{\mathit{\_}\mathit{C}\mathit{2}}^2-1)}^{-1}}\}$$