68.1.51 problem 58

Internal problem ID [17118]
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 : Thursday, October 02, 2025 at 01:43:25 PM
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*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 10

ode:=diff(y(x),x) = ln(x)/x; 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to \frac {\log ^2(x)}{2} \end{align*}

✓ Sympy. Time used: 0.127 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - log(x)/x,0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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