44.5.13 problem 13

Internal problem ID [7075]
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 : 13
Date solved : Monday, January 27, 2025 at 02:47:09 PM
CAS classification : [_separable]

\begin{align*} \left (1+{\mathrm e}^{y}\right )^{2} {\mathrm e}^{-y}+\left ({\mathrm e}^{x}+1\right )^{3} {\mathrm e}^{-x} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 53

dsolve((exp(y(x))+1)^2*exp(-y(x))+(exp(x)+1)^3*exp(-x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \ln \left (-\frac {-3+2 \,{\mathrm e}^{2 x} c_{1} -2 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{x} c_{1} -4 \,{\mathrm e}^{x}+2 c_{1}}{2 \,{\mathrm e}^{2 x} c_{1} +4 \,{\mathrm e}^{x} c_{1} +2 c_{1} -1}\right ) \]

✓ Solution by Mathematica

Time used: 4.662 (sec). Leaf size: 35

DSolve[(Exp[y[x]]+1)^2*Exp[-y[x]]+(Exp[x]+1)^3*Exp[-x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \log \left (-1-\frac {1}{\frac {1}{2 \left (e^x+1\right )^2}+c_1}\right ) \\ y(x)\to i \pi \\ \end{align*}