54.2.111 problem 687

Internal problem ID [11985]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 687
Date solved : Tuesday, September 30, 2025 at 11:51:54 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

\begin{align*} y^{\prime }&=\frac {y-\ln \left (\frac {x +1}{x -1}\right ) x^{3}+\ln \left (\frac {x +1}{x -1}\right ) x y^{2}}{x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 39

ode:=diff(y(x),x) = (y(x)-ln((1+x)/(x-1))*x^3+ln((1+x)/(x-1))*x*y(x)^2)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\tanh \left (\frac {x^{2} \ln \left (\frac {x +1}{x -1}\right )}{2}-\frac {\ln \left (\frac {x +1}{x -1}\right )}{2}+c_1 +x -1\right ) x \]

✓ Mathematica. Time used: 0.083 (sec). Leaf size: 69

ode=D[y[x],x] == (-(x^3*Log[(1 + x)/(-1 + x)]) + y[x] + x*Log[(1 + x)/(-1 + x)]*y[x]^2)/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{(K[1]-1) (K[1]+1)}dK[1]=\frac {1}{2} \left (x^2 (-\log (x-1))+x^2 \log (x+1)+2 x+\log (1-x)-\log (x+1)\right )+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (-x**3*log((x + 1)/(x - 1)) + x*y(x)**2*log((x + 1)/(x - 1)) + y(x))/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out