72.1.20 problem 23

Internal problem ID [14541]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.2. page 33
Problem number : 23
Date solved : Thursday, March 13, 2025 at 03:33:06 AM
CAS classification : [_separable]

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

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

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

\[ w = c_{1} t \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 14

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

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

✓ Sympy. Time used: 0.098 (sec). Leaf size: 5

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

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