78.1.35 problem 3 (c)

Internal problem ID [18090]
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 : Tuesday, January 28, 2025 at 11:25:59 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*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 11

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

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