44.4.46 problem 28

Internal problem ID [7059]
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 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 28
Date solved : Monday, January 27, 2025 at 02:46:30 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\left (y \,{\mathrm e}^{y}-9 y\right ) {\mathrm e}^{-y} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

dsolve(diff(y(x),x)=(y(x)*exp(y(x))-9*y(x))/exp(y(x)),y(x), singsol=all)
 

\[ x +\int _{}^{y}\frac {1}{\textit {\_a} \left (9 \,{\mathrm e}^{-\textit {\_a}}-1\right )}d \textit {\_a} +c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.660 (sec). Leaf size: 47

DSolve[D[y[x],x]==(y[x]*Exp[y[x]]-9*y[x])/Exp[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {e^{K[1]}}{\left (-9+e^{K[1]}\right ) K[1]}dK[1]\&\right ][x+c_1] \\ y(x)\to 0 \\ y(x)\to \log (9) \\ \end{align*}