60.2.217 problem 793

Internal problem ID [10791]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 793
Date solved : Sunday, March 30, 2025 at 06:53:58 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 25

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

\[ y = \frac {\operatorname {LambertW}\left (-\frac {2 \left (x -1\right ) {\mathrm e}^{3 c_1 -1}}{x}\right )}{x -1} \]

✓ Mathematica. Time used: 1.271 (sec). Leaf size: 111

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

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

✗ Sympy

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

Timed Out