66.2.20 problem Problem 20

Internal problem ID [13848]
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 : Monday, March 31, 2025 at 08:15:07 AM
CAS classification : [[_2nd_order, _missing_y]]

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

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

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

\[ u = c_1 +\frac {c_2}{r} \]

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

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

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

✓ Sympy. Time used: 0.131 (sec). Leaf size: 7

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

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