86.1.5 problem 5

Internal problem ID [23067]
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 3b at page 43
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:18:38 PM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=\frac {x}{t} \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 7

ode:=diff(x(t),t) = x(t)/t; 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 t \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 14

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

\begin{align*} x(t)&\to c_1 t\\ x(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.053 (sec). Leaf size: 5

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

\[ x{\left (t \right )} = C_{1} t \]