44.4.45 problem 27

Internal problem ID [7058]
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 : 27
Date solved : Monday, January 27, 2025 at 02:46:28 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y \ln \left (y+2\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x)=y(x)*ln(y(x)+2),y(x), singsol=all)
 

\[ x -\int _{}^{y}\frac {1}{\textit {\_a} \ln \left (2+\textit {\_a} \right )}d \textit {\_a} +c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.590 (sec). Leaf size: 41

DSolve[D[y[x],x]==y[x]*Log[y[x]+2],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1] \log (K[1]+2)}dK[1]\&\right ][x+c_1] \\ y(x)\to -1 \\ y(x)\to 0 \\ \end{align*}