2.714   ODE No. 714

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

$$y^{\prime }(x)=-\frac{y(x)(x^{3}y(x)+x^{2}y(x)\log (x)-x^2+e^x-x\log (x)-\log \left(\frac{1}{x}\right))}{x(e^x-\log \left(\frac{1}{x}\right))}$$ ✓ Mathematica : cpu = 1.34968 (sec), leaf count = 162

$$\left\{\{y(x)\to \frac{\exp ({\int }_1^x-\frac{-K[1{]}^2-\log (K[1])K[1]+e^{K[1]}-\log \left(\frac{1}{K[1]}\right)}{K[1](e^{K[1]}-\log \left(\frac{1}{K[1]}\right))}dK[1])}{-{\int }_1^x-\frac{\exp ({\int }_1^{K[2]}-\frac{-K[1{]}^2-\log (K[1])K[1]+e^{K[1]}-\log \left(\frac{1}{K[1]}\right)}{K[1](e^{K[1]}-\log \left(\frac{1}{K[1]}\right))}dK[1])(K[2{]}^3+\log (K[2])K[2{]}^2)}{K[2](e^{K[2]}-\log \left(\frac{1}{K[2]}\right))}dK[2]+c_1}\}\right\}$$ ✓ Maple : cpu = 0.362 (sec), leaf count = 96

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