44.1.10 problem 11

Internal problem ID [6885]
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 : 11
Date solved : Monday, January 27, 2025 at 02:33:56 PM
CAS classification : [_separable]

\begin{align*} y^{2}-1+x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 9

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

\[ y = \tanh \left (\ln \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.583 (sec). Leaf size: 40

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

\begin{align*} y(x)\to \frac {x^2-e^{2 c_1}}{x^2+e^{2 c_1}} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}