72.1.35 problem 3 (c)

Internal problem ID [19376]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 3 (c)
Date solved : Thursday, October 02, 2025 at 04:19:59 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left ({\mathrm e}\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 10

ode:=diff(y(x),x) = ln(x); 
ic:=[y(exp(1)) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x \left (\ln \left (x \right )-1\right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 11

ode=D[y[x],x]==Log[x]; 
ic={y[Exp[1]]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x (\log (x)-1) \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = x \log {\left (x \right )} - x \]