15.3.6 problem 6

Internal problem ID [2899]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 7, page 28
Problem number : 6
Date solved : Tuesday, March 04, 2025 at 03:06:28 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 30

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

\[ y = \tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x -1\right )+2 c_1 \right )\right ) \left (1-x \right ) \]

✓ Mathematica. Time used: 0.059 (sec). Leaf size: 48

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

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

✗ Sympy

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

RecursionError : maximum recursion depth exceeded