3.151   ODE No. 151

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

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

Mathematica: cpu = 0.420553 (sec), leaf count = 203 $$\text{Solve}[c_1=\frac{\frac{1}{2}(\frac{1}{\frac{ix}{x^2+1}-\frac{i{x}^{2}y(x)}{x^2+1}}+\frac{i}{x})\sqrt[4]{1-{(\frac{1}{\frac{ix}{x^2+1}-\frac{i{x}^{2}y(x)}{x^2+1}}+\frac{i}{x})}^2}{}_2{F}_1(\frac{1}{2},\frac{5}{4};\frac{3}{2};{(\frac{1}{\frac{ix}{x^2+1}-\frac{i{x}^{2}y(x)}{x^2+1}}+\frac{i}{x})}^2)+ix}{\sqrt[4]{-1+{(\frac{1}{\frac{ix}{x^2+1}-\frac{i{x}^{2}y(x)}{x^2+1}}+\frac{i}{x})}^2}},y(x)]$$

Maple: cpu = 0.047 (sec), leaf count = 85 $$\{\mathit{\_}\mathit{C}\mathit{1}+x\frac{1}{\sqrt[4]{{(x^{-1}+x^2{(\frac{y\left(x\right)x^4}{x^2+1}-\frac{x^3}{x^2+1})}^{-1})}^2+1}}+\frac{y\left(x\right)+x}{2xy\left(x\right)-2}{}_2\text{F}{}_1(\frac{1}{2},\frac{5}{4};\frac{3}{2};-\frac{{(y\left(x\right)+x)}^2}{{(xy\left(x\right)-1)}^2})=0\}$$