44.5.24 problem 24

Internal problem ID [7086]
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 : 24
Date solved : Tuesday, January 28, 2025 at 08:48:15 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (2\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 5

dsolve([diff(y(x),x)=(y(x)^2-1)/(x^2-1),y(2) = 2],y(x), singsol=all)
 

\[ y = x \]

✓ Solution by Mathematica

Time used: 4.048 (sec). Leaf size: 6

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

\[ y(x)\to x \]