56.5.23 problem 23

Internal problem ID [8984]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 23
Date solved : Sunday, March 30, 2025 at 01:57:59 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {x y+3 x -2 y+6}{x y-3 x -2 y+6} \end{align*}

✗ Maple

ode:=diff(y(x),x) = (x*y(x)+3*x-2*y(x)+6)/(x*y(x)-3*x-2*y(x)+6); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]==(x*y[x]+3*x-2*y[x]+6)/(x*y[x]-3*x-2*y[x]+6); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x*y(x) + 3*x - 2*y(x) + 6)/(x*y(x) - 3*x - 2*y(x) + 6),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out