ODE No. 789

$$y^{\prime }(x)=\frac{x^2\coth (x+1)+2xy(x)\coth (x+1)+y(x{)}^2\coth (x+1)-\log (x-1)+\coth (x+1)}{\log (x-1)}$$ ✓ Mathematica : cpu = 57.3856 (sec), leaf count = 120

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

$$\left\{\{y(x)\to -\frac{e^{2}x\sinh (x)-x\sinh (x)+e^{2}x\cosh (x)+x\cosh (x)}{e^2\sinh (x)-\sinh (x)+e^2\cosh (x)+\cosh (x)}+\tan ({\int }_1^x\frac{e^2\cosh (K[5])+\cosh (K[5])+e^2\sinh (K[5])-\sinh (K[5])}{\log (K[5]-1)(e^2\cosh (K[5])-\cosh (K[5])+e^2\sinh (K[5])+\sinh (K[5]))}dK[5]+c_1)\}\right\}$$ ✗ Maple : cpu = 0. (sec), leaf count = 0

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

, could not solve

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