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 : Tuesday, February 04, 2025 at 12:14:24 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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