44.5.69 problem 58 (a 1)

Internal problem ID [7131]
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 : 58 (a 1)
Date solved : Sunday, March 30, 2025 at 11:48:12 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left ({\mathrm e}\right )&=1 \end{align*}

✓ Maple. Time used: 0.031 (sec). Leaf size: 14

ode:=diff(y(x),x) = y(x)+y(x)/x/ln(x); 
ic:=y(exp(1)) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 15

ode=D[y[x],x]==y[x]+y[x]/(x*Log[x]); 
ic={y[Exp[1]]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{x-e} \log (x) \]

✓ Sympy. Time used: 0.273 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + Derivative(y(x), x) - y(x)/(x*log(x)),0) 
ics = {y(E): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {e^{x} \log {\left (x \right )}}{e^{e}} \]