87.4.21 problem 32

Internal problem ID [23287]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 37
Problem number : 32
Date solved : Thursday, October 02, 2025 at 09:28:41 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }-\frac {y}{\ln \left (x \right )}&=0 \end{align*}

With initial conditions

\begin{align*} y \left ({\mathrm e}\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 8

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

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 9

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

\begin{align*} y(x)&\to -\log (x) \end{align*}

✓ Sympy. Time used: 0.138 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = - \log {\left (x \right )} \]