3.259   ODE No. 259

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

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

Mathematica: cpu = 0.019002 (sec), leaf count = 50 $$\{\{y(x)\to -e^{-\frac{1}{2}/x}\sqrt{c_1+e^x}\},\{y(x)\to e^{-\frac{1}{2}/x}\sqrt{c_1+e^x}\}\}$$

Maple: cpu = 0.032 (sec), leaf count = 51 $$\{y\left(x\right)=\sqrt{{\mathrm{e}}^{-x^{-1}}\mathit{\_}\mathit{C}\mathit{1}+{\mathrm{e}}^{\frac{x^2-1}{x}}},y\left(x\right)=-\sqrt{{\mathrm{e}}^{-x^{-1}}\mathit{\_}\mathit{C}\mathit{1}+{\mathrm{e}}^{\frac{x^2-1}{x}}}\}$$