89.1.7 problem 7

Internal problem ID [24242]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 21
Problem number : 7
Date solved : Thursday, October 02, 2025 at 10:01:23 PM
CAS classification : [_separable]

\begin{align*} v^{\prime }&=-\frac {v}{p} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

ode:=diff(v(p),p) = -v(p)/p; 
dsolve(ode,v(p), singsol=all);
 

\[ v = \frac {c_1}{p} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 16

ode=D[v[p],{p,1}]==-v[p]/p; 
ic={}; 
DSolve[{ode,ic},v[p],p,IncludeSingularSolutions->True]
 

\begin{align*} v(p)&\to \frac {c_1}{p}\\ v(p)&\to 0 \end{align*}

✓ Sympy. Time used: 0.056 (sec). Leaf size: 5

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

\[ v{\left (p \right )} = \frac {C_{1}}{p} \]