66.2.20 problem Problem 20

Internal problem ID [13919]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 20
Date solved : Tuesday, January 28, 2025 at 06:08:36 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 15

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

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