Internal problem ID [10835]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {u^{\prime \prime }+\frac {2 u^{\prime }}{r}=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.012 (sec). Leaf size: 15
DSolve[u''[r]+2/r*u'[r]==0,u[r],r,IncludeSingularSolutions -> True]
\begin{align*} u(r)\to c_2-\frac {c_1}{r} \\ \end{align*}