44.5.37 problem 37

Internal problem ID [7099]
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 : 37
Date solved : Wednesday, March 05, 2025 at 04:10:31 AM
CAS classification : [_separable]

\begin{align*} {\mathrm e}^{y}-{\mathrm e}^{-x} y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 13

ode:=exp(y(x))-exp(-x)*diff(y(x),x) = 0; 
ic:=y(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\ln \left (-{\mathrm e}^{x}+2\right ) \]

✓ Mathematica. Time used: 1.206 (sec). Leaf size: 15

ode=Exp[y[x]]-Exp[-x]*D[y[x],x]==0; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\log \left (2-e^x\right ) \]

✓ Sympy. Time used: 0.256 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \log {\left (- \frac {1}{e^{x} - 2} \right )} \]