60.2.260 problem 836

Internal problem ID [10834]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 836
Date solved : Sunday, March 30, 2025 at 07:11:20 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class C`]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 48

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

\[ y = -\frac {x}{-9 \,{\mathrm e}^{-\operatorname {RootOf}\left (-{\mathrm e}^{\textit {\_Z}} \ln \left ({\mathrm e}^{\textit {\_Z}}+9\right )+{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )+3 c_1 \,{\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} x +9\right )}+x -1} \]

✓ Mathematica. Time used: 1.375 (sec). Leaf size: 105

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

\[ \text {Solve}\left [\int _1^{\frac {(x-1)^2 \left (\frac {x^6}{(x-1)^3}\right )^{2/3} (x+(x+2) y(x))}{\sqrt [3]{2} x^4 (x+(x-1) y(x))}}\frac {1}{K[1]^3-\frac {3 K[1]}{2^{2/3}}+1}dK[1]+\frac {2^{2/3} \left (\frac {x^6}{(x-1)^3}\right )^{2/3} (x-1)^2}{9 x^3}=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out