3.251   ODE No. 251

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

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

Mathematica: cpu = 0.011501 (sec), leaf count = 60 $$\{\{y(x)\to \frac{1}{x^2}-\frac{\sqrt{c_1{x}^2+2x^3+1}}{x^2}\},\{y(x)\to \frac{\sqrt{c_1{x}^2+2x^3+1}}{x^2}+\frac{1}{x^2}\}\}$$

Maple: cpu = 0.032 (sec), leaf count = 50 $$\{y\left(x\right)=\frac{1}{x^2}(1+\sqrt{-2x^2\mathit{\_}\mathit{C}\mathit{1}+2x^3+1}),y\left(x\right)=-\frac{1}{x^2}(-1+\sqrt{-2x^2\mathit{\_}\mathit{C}\mathit{1}+2x^3+1})\}$$