74.1.51 problem 58

Internal problem ID [15831]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 58
Date solved : Tuesday, January 28, 2025 at 08:08:28 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 10

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

\[ y = \frac {\ln \left (x \right )^{2}}{2} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 13

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

\[ y(x)\to \frac {\log ^2(x)}{2} \]