29.8.4 problem 4

Internal problem ID [7346]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 04:29:18 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} r^{\prime \prime }-6 r^{\prime }+9 r&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=diff(diff(r(t),t),t)-6*diff(r(t),t)+9*r(t) = 0; 
dsolve(ode,r(t), singsol=all);
 

\[ r = {\mathrm e}^{3 t} \left (c_2 t +c_1 \right ) \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 18

ode=D[r[t],{t,2}]-6*D[r[t],t]+9*r[t]==0; 
ic={}; 
DSolve[{ode,ic},r[t],t,IncludeSingularSolutions->True]
 

\begin{align*} r(t)&\to e^{3 t} (c_2 t+c_1) \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
r = Function("r") 
ode = Eq(9*r(t) - 6*Derivative(r(t), t) + Derivative(r(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=r(t),ics=ics)
 

\[ r{\left (t \right )} = \left (C_{1} + C_{2} t\right ) e^{3 t} \]