44.5.22 problem 22

Internal problem ID [7084]
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 : 22
Date solved : Monday, January 27, 2025 at 02:48:01 PM
CAS classification : [_separable]

\begin{align*} \left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime }&=y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 13

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

\[ y = \frac {1}{-\arctan \left ({\mathrm e}^{x}\right )+c_{1}} \]

✓ Solution by Mathematica

Time used: 0.298 (sec). Leaf size: 21

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

\begin{align*} y(x)\to -\frac {1}{\arctan \left (e^x\right )+c_1} \\ y(x)\to 0 \\ \end{align*}