86.2.10 problem 10

Internal problem ID [23084]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 3. Some standard types of differential equations. Exercise 3c at page 50
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:19:39 PM
CAS classification : [_linear]

\begin{align*} \frac {y}{x}+\ln \left (x \right ) y^{\prime }&=2 \end{align*}

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

ode:=y(x)/x+ln(x)*diff(y(x),x) = 2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 x +c_1}{\ln \left (x \right )} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 16

ode=y[x]/x+Log[x]*D[y[x],x]==2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 x+c_1}{\log (x)} \end{align*}

✓ Sympy. Time used: 0.171 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(log(x)*Derivative(y(x), x) - 2 + y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + 2 x}{\log {\left (x \right )}} \]