81.4.18 problem 5-19

Internal problem ID [21532]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 5. Integrating factors. Page 72.
Problem number : 5-19
Date solved : Thursday, October 02, 2025 at 07:46:58 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 13

ode:=ln(y(x))+1/y(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {{\mathrm e}^{-x}}{c_1}} \]

✓ Mathematica. Time used: 0.159 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to e^{e^{-x+c_1}}\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.162 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = e^{C_{1} e^{- x}} \]