2.783   ODE No. 783

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

$$y^{\prime }(x)=-\frac{y(x)\coth (x)(x^{2}y(x)(-\log (2x))+x\log (2x)+\tanh (x))}{x}$$ ✓ Mathematica : cpu = 4.52942 (sec), leaf count = 88

$$\left\{\{y(x)\to \frac{\exp ({\int }_1^x\frac{-\coth (K[1])K[1]\log (2K[1])-1}{K[1]}dK[1])}{-{\int }_1^x\exp ({\int }_1^{K[2]}\frac{-\coth (K[1])K[1]\log (2K[1])-1}{K[1]}dK[1])\coth (K[2])K[2]\log (2K[2])dK[2]+c_1}\}\right\}$$ ✓ Maple : cpu = 0.2 (sec), leaf count = 75

$$\{y\left(x\right)=\frac{{\mathrm{e}}^{\int \frac{-x\ln \left(x\right)-\ln \left(2\right)x-\tanh \left(x\right)}{x\tanh \left(x\right)}dx}}{c_1+\int -\frac{(\ln \left(x\right)+\ln \left(2\right))x{\mathrm{e}}^{\int \frac{-x\ln \left(x\right)-\ln \left(2\right)x-\tanh \left(x\right)}{x\tanh \left(x\right)}dx}}{\tanh \left(x\right)}dx}\}$$