54.2.119 problem 695

Internal problem ID [11993]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 695
Date solved : Tuesday, September 30, 2025 at 11:52:24 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

\begin{align*} y^{\prime }&=\frac {y \ln \left (x -1\right )+x^{4}+x^{3}+x^{2} y^{2}+x y^{2}}{\ln \left (x -1\right ) x} \end{align*}

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

ode:=diff(y(x),x) = (y(x)*ln(x-1)+x^4+x^3+x^2*y(x)^2+x*y(x)^2)/ln(x-1)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \tan \left (-\operatorname {Ei}_{1}\left (-3 \ln \left (x -1\right )\right )-3 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x -1\right )\right )-2 \,\operatorname {Ei}_{1}\left (-\ln \left (x -1\right )\right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.093 (sec). Leaf size: 48

ode=D[y[x],x] == (x^3 + x^4 + Log[-1 + x]*y[x] + x*y[x]^2 + x^2*y[x]^2)/(x*Log[-1 + x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**4 + x**3 + x**2*y(x)**2 + x*y(x)**2 + y(x)*log(x - 1))/(x*log(x - 1)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out