38.5.22 problem 22

Internal problem ID [8370]
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 : Tuesday, September 30, 2025 at 05:30:53 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

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

\[ y = \frac {1}{-\arctan \left ({\mathrm e}^{x}\right )+c_1} \]

✓ Mathematica. Time used: 0.183 (sec). Leaf size: 21

ode=(Exp[x]+Exp[-x])*D[y[x],x]==y[x]^2; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.288 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((exp(x) + exp(-x))*Derivative(y(x), x) - y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {1}{C_{1} + \operatorname {atan}{\left (\tanh {\left (\frac {x}{2} \right )} \right )}} \]