27.1.3 problem 3

Internal problem ID [4297]
Book : An introduction to the solution and applications of differential equations, J.W. Searl, 1966
Section : Chapter 4, Ex. 4.1
Problem number : 3
Date solved : Sunday, March 30, 2025 at 02:52:44 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y = \frac {-x +c_1}{\ln \left (x \right )} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 16

ode=Log[x]*D[y[x],x]+(x+y[x])/x==0; 
DSolve[ode,y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {-x+c_1}{\log (x)} \]

✓ Sympy. Time used: 0.251 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = \frac {C_{1} - x}{\log {\left (x \right )}} \]