Internal problem ID [8369]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 789.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {\ln \left (x -1\right )-\coth \left (x +1\right ) x^{2}-2 \coth \left (x +1\right ) y x -\coth \left (x +1\right )-\coth \left (x +1\right ) y^{2}}{\ln \left (x -1\right )}=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x) = -(ln(x-1)-coth(x+1)*x^2-2*coth(x+1)*x*y(x)-coth(x+1)-coth(x+1)*y(x)^2)/ln(x-1),y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 83.043 (sec). Leaf size: 46
DSolve[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,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+\tan \left (\int _1^x\frac {1}{\left (1-\frac {2}{1+e^{2 K[5]+2}}\right ) \log (K[5]-1)}dK[5]+c_1\right ) \\ \end{align*}