2.1283   ODE No. 1283

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

$$4x^2\log (x)y^{\prime }(x)+4x^2{y}^{″}(x)+y(x)(x^2{\log }^2(x)+2x-8)-4\sqrt{e^x{x}^{-x}}{x}^2=0$$ ✓ Mathematica : cpu = 0.0686383 (sec), leaf count = 90

$$\left\{\{y(x)\to \frac{1}{9}(3x^2\sqrt{e^x{x}^{-x}}\log (x)-x^2\sqrt{e^x{x}^{-x}})+c_1{e}^{x/2}{x}^{-\frac{x}{2}-1}+\frac{1}{3}{c}_2{e}^{x/2}{x}^{2-\frac{x}{2}}\}\right\}$$ ✓ Maple : cpu = 0.167 (sec), leaf count = 48

$$\{y\left(x\right)=\frac{x^2}{3}(\ln \left(x\right)-\frac{1}{3})\sqrt{x^{-x}{\mathrm{e}}^x}+{\mathrm{e}}^{\frac{x}{2}}(\mathit{\_}\mathit{C}\mathit{1}{x}^{-\frac{x}{2}+2}+\mathit{\_}\mathit{C}\mathit{2}{x}^{-\frac{x}{2}-1})\}$$