86.2.12 problem 12

Internal problem ID [23086]
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 : 12
Date solved : Thursday, October 02, 2025 at 09:19:45 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=1+\frac {y}{x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

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

\[ y = \left (\ln \left (x \right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 12

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

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

✓ Sympy. Time used: 0.088 (sec). Leaf size: 8

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

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