50.1.27 problem 3(c)

Internal problem ID [7799]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 3(c)
Date solved : Wednesday, March 05, 2025 at 05:06:16 AM
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: 0.006 (sec). Leaf size: 10

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

\[ y(x)\to x (\log (x)-1) \]

✓ Sympy. Time used: 0.133 (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)
 

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