83.1.2 problem 3

Internal problem ID [18975]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter I. Introduction and definitions. Exercise I at page 5
Problem number : 3
Date solved : Monday, March 31, 2025 at 06:27:52 PM
CAS classification : [[_2nd_order, _missing_y]]

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

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

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

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 15

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

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

✓ Sympy. Time used: 0.128 (sec). Leaf size: 7

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

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