60.2.213 problem 789

Internal problem ID [10800]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 789
Date solved : Monday, January 27, 2025 at 09:49:49 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} y^{\prime }&=-\frac {\ln \left (x -1\right )-\coth \left (1+x \right ) x^{2}-2 \coth \left (1+x \right ) x y-\coth \left (1+x \right )-\coth \left (1+x \right ) y^{2}}{\ln \left (x -1\right )} \end{align*}

✗ 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: 3.394 (sec). Leaf size: 68

DSolve[D[y[x],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]
 

\[ y(x)\to -x+\tan \left (\int _1^x\frac {\left (1+e^2\right ) \cosh (K[5])+\left (-1+e^2\right ) \sinh (K[5])}{\log (K[5]-1) \left (\left (-1+e^2\right ) \cosh (K[5])+\left (1+e^2\right ) \sinh (K[5])\right )}dK[5]+c_1\right ) \]