38.5.4 problem 4

Internal problem ID [8352]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 05:29:34 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-\left (y-1\right )^{2}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

ode:=diff(y(x),x)-(y(x)-1)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 +x -1}{c_1 +x} \]

✓ Mathematica. Time used: 0.077 (sec). Leaf size: 22

ode=D[y[x],x]-(y[x]-1)^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x-1+c_1}{x+c_1}\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {C_{1} - x + 1}{C_{1} - x} \]