38.1.41 problem 43

Internal problem ID [8202]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 43
Date solved : Tuesday, September 30, 2025 at 05:18:44 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

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

\begin{align*} y &= 1-\sqrt {1+2 c_1 +2 x} \\ y &= 1+\sqrt {1+2 c_1 +2 x} \\ \end{align*}

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 41

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

\begin{align*} y(x)&\to 1-\sqrt {2 x+1+2 c_1}\\ y(x)&\to 1+\sqrt {2 x+1+2 c_1} \end{align*}

✓ Sympy. Time used: 0.210 (sec). Leaf size: 24

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

\[ \left [ y{\left (x \right )} = 1 - \sqrt {C_{1} + 2 x}, \ y{\left (x \right )} = \sqrt {C_{1} + 2 x} + 1\right ] \]