44.1.41 problem 43

Internal problem ID [6916]
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 : Monday, January 27, 2025 at 02:34:55 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

dsolve((y(x)-1)*diff(y(x),x)=1,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*}

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 41

DSolve[(y[x]-1)*D[y[x],x]==1,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*}