26.2.5 problem Differential equations with Linear Coefficients. Exercise 8.5, page 69

Internal problem ID [6924]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 8
Problem number : Differential equations with Linear Coefficients. Exercise 8.5, page 69
Date solved : Tuesday, September 30, 2025 at 04:05:57 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y-1-\left (x -y-1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 30

ode:=x+y(x)-1-(x-y(x)-1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 48

ode=(x+y[x]-1)-(x-y[x]-1)*D[y[x],x]==0; 
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(x - (x - y(x) - 1)*Derivative(y(x), x) + y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded