60.2.127 problem 703

Internal problem ID [10701]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 703
Date solved : Sunday, March 30, 2025 at 06:22:47 PM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

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

\[ y = \frac {1}{x \left (1+{\mathrm e}^{x -\operatorname {dilog}\left (x \right )} c_1 \left (x -1\right )\right )} \]

✓ Mathematica. Time used: 1.074 (sec). Leaf size: 168

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

\begin{align*} y(x)\to \frac {e^{-\operatorname {PolyLog}(2,x)-x} (1-x)^{-\log (x)-1}}{x \left (-\int _1^xe^{-K[1]-\operatorname {PolyLog}(2,K[1])} (1-K[1])^{-\log (K[1])-2} (-K[1]-\log (K[1]))dK[1]+c_1\right )} \\ y(x)\to 0 \\ y(x)\to -\frac {e^{-\operatorname {PolyLog}(2,x)-x} (1-x)^{-\log (x)-1}}{x \int _1^xe^{-K[1]-\operatorname {PolyLog}(2,K[1])} (1-K[1])^{-\log (K[1])-2} (-K[1]-\log (K[1]))dK[1]} \\ \end{align*}

✗ Sympy

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

Timed Out