60.2.213 problem 789

Internal problem ID [10787]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 789
Date solved : Wednesday, March 05, 2025 at 12:42:19 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

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

✗ Maple

ode:=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); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 3.394 (sec). Leaf size: 68

ode=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]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x**2/tanh(x + 1) - 2*x*y(x)/tanh(x + 1) - y(x)**2/tanh(x + 1) + log(x - 1) - 1/tanh(x + 1))/log(x - 1) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

IndexError : Index out of range: a[1]