ODE No. 776

$$y^{\prime }(x)=\frac{y(x)(x^{2}y(x)\log \left(\frac{x^2+1}{x}\right)-x\log \left(\frac{x^2+1}{x}\right)-\log \left(\frac{1}{x}\right))}{x\log \left(\frac{1}{x}\right)}$$ ✓ Mathematica : cpu = 0.378235 (sec), leaf count = 133

DSolve[Derivative[1][y][x] == (y[x]*(-Log[x^(-1)] - x*Log[(1 + x^2)/x] + x^2*Log[(1 + x^2)/x]*y[x]))/(x*Log[x^(-1)]),y[x],x]
 

$$\left\{\{y(x)\to \frac{\exp ({\int }_1^x\frac{-\log \left(\frac{1}{K[1]}\right)-K[1]\log \left(\frac{K[1{]}^2+1}{K[1]}\right)}{K[1]\log \left(\frac{1}{K[1]}\right)}dK[1])}{-{\int }_1^x\frac{\exp ({\int }_1^{K[2]}\frac{-\log \left(\frac{1}{K[1]}\right)-K[1]\log \left(\frac{K[1{]}^2+1}{K[1]}\right)}{K[1]\log \left(\frac{1}{K[1]}\right)}dK[1])K[2]\log \left(\frac{K[2{]}^2+1}{K[2]}\right)}{\log \left(\frac{1}{K[2]}\right)}dK[2]+c_1}\}\right\}$$ ✓ Maple : cpu = 0.246 (sec), leaf count = 96

dsolve(diff(y(x),x) = y(x)*(-ln(1/x)-ln((x^2+1)/x)*x+ln((x^2+1)/x)*x^2*y(x))/x/ln(1/x),y(x))
 

$$y\left(x\right)=\frac{{\mathrm{e}}^{\int \frac{-\ln \left(\frac{x^2+1}{x}\right)x-\ln \left(\frac{1}{x}\right)}{x\ln \left(\frac{1}{x}\right)}dx}}{\int -\frac{{\mathrm{e}}^{\int \frac{-\ln \left(\frac{x^2+1}{x}\right)x-\ln \left(\frac{1}{x}\right)}{x\ln \left(\frac{1}{x}\right)}dx}\ln \left(\frac{x^2+1}{x}\right)x}{\ln \left(\frac{1}{x}\right)}dx+c_1}$$