38.4.45 problem 27

Internal problem ID [8344]
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 : Tuesday, September 30, 2025 at 05:29:26 PM
CAS classification : [_quadrature]

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

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

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

\[ x -\int _{}^{y}\frac {1}{\textit {\_a} \ln \left (\textit {\_a} +2\right )}d \textit {\_a} +c_1 = 0 \]

✓ Mathematica. Time used: 0.135 (sec). Leaf size: 41

ode=D[y[x],x]==y[x]*Log[y[x]+2]; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.222 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)*log(y(x) + 2) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \int \limits ^{y{\left (x \right )}} \frac {1}{y \log {\left (y + 2 \right )}}\, dy = C_{1} + x \]