81.1.13 problem 12

Internal problem ID [18529]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter I. Introduction. Exercises at page 13
Problem number : 12
Date solved : Thursday, March 13, 2025 at 12:11:52 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} v^{\prime \prime }+\frac {2 v^{\prime }}{r}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 11

ode:=diff(diff(v(r),r),r)+2/r*diff(v(r),r) = 0; 
dsolve(ode,v(r), singsol=all);
 

\[ v \left (r \right ) = c_{1} +\frac {c_{2}}{r} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 15

ode=D[v[r],{r,2}]+2/r*D[v[r],r]==0; 
ic={}; 
DSolve[{ode,ic},v[r],r,IncludeSingularSolutions->True]
 

\[ v(r)\to c_2-\frac {c_1}{r} \]

✓ Sympy. Time used: 0.136 (sec). Leaf size: 7

from sympy import * 
r = symbols("r") 
v = Function("v") 
ode = Eq(Derivative(v(r), (r, 2)) + 2*Derivative(v(r), r)/r,0) 
ics = {} 
dsolve(ode,func=v(r),ics=ics)
 

\[ v{\left (r \right )} = C_{1} + \frac {C_{2}}{r} \]