68.4.26 problem 26

Internal problem ID [17206]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 26
Date solved : Thursday, October 02, 2025 at 01:53:15 PM
CAS classification : [_separable]

\begin{align*} \frac {x -2}{x^{2}-4 x +3}&=\frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 1004

ode:=(x-2)/(x^2-4*x+3) = (1-1/y(x))^2/y(x)^2*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 21.447 (sec). Leaf size: 1539

ode=(x-2)/(x^2-4*x+3)==(1-1/y[x])^2*1/y[x]^2*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(1 - 1/y(x))**2*Derivative(y(x), x)/y(x)**2 + (x - 2)/(x**2 - 4*x + 3),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out