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 : Monday, January 27, 2025 at 03:23:25 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*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 10

dsolve([diff(y(x),x)=ln(x),y(exp(1)) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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