75.7.13 problem 14

Internal problem ID [19995]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter VI. Certain particular forms of equations. Exercises at page 74
Problem number : 14
Date solved : Thursday, October 02, 2025 at 05:06:16 PM
CAS classification : [[_2nd_order, _missing_y]]

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

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

ode:=diff(diff(V(r),r),r)+1/r*diff(V(r),r) = 0; 
dsolve(ode,V(r), singsol=all);
 

\[ V = c_2 \ln \left (r \right )+c_1 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 13

ode=D[V[r],{r,2}]+1/r*D[V[r],r]==0; 
ic={}; 
DSolve[{ode,ic},V[r],r,IncludeSingularSolutions->True]
 

\begin{align*} V(r)&\to c_1 \log (r)+c_2 \end{align*}

✓ Sympy. Time used: 0.072 (sec). Leaf size: 8

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

\[ V{\left (r \right )} = C_{1} + C_{2} \log {\left (r \right )} \]