81.7.13 problem 14

Internal problem ID [18710]
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 : Tuesday, January 28, 2025 at 12:12:10 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

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

dsolve(diff(V(r),r$2)+1/r*diff(V(r),r)=0,V(r), singsol=all)
 

\[ V \left (r \right ) = c_{2} \ln \left (r \right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 13

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

\[ V(r)\to c_1 \log (r)+c_2 \]