Internal problem ID [5378]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\ln \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \left ({\mathrm e}\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([diff(y(x),x)=ln(x),y(exp(1)) = 0],y(x), singsol=all)
\[ y \relax (x ) = x \left (\ln \relax (x )-1\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 11
DSolve[{y'[x]==Log[x],{y[Exp[1]]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (\log (x)-1) \\ \end{align*}