44.5.4 problem 4

Internal problem ID [7066]
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 : Monday, January 27, 2025 at 02:46:39 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.103 (sec). Leaf size: 22

DSolve[D[y[x],x]-(y[x]-1)^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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