80.6.22 problem 22

Internal problem ID [21312]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 6. Higher order linear equations. Excercise 6.5 at page 133
Problem number : 22
Date solved : Thursday, October 02, 2025 at 07:28:21 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} x^{\left (6\right )}-64 x&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 53

ode:=diff(diff(diff(diff(diff(diff(x(t),t),t),t),t),t),t)-64*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = \left (\left ({\mathrm e}^{3 t} c_6 +c_4 \,{\mathrm e}^{t}\right ) \cos \left (\sqrt {3}\, t \right )+\left ({\mathrm e}^{3 t} c_5 +c_3 \,{\mathrm e}^{t}\right ) \sin \left (\sqrt {3}\, t \right )+c_1 \,{\mathrm e}^{4 t}+c_2 \right ) {\mathrm e}^{-2 t} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 68

ode=D[x[t],{t,6}]-64*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to e^{-2 t} \left (c_1 e^{4 t}+e^t \left (c_2 e^{2 t}+c_3\right ) \cos \left (\sqrt {3} t\right )+e^t \left (c_6 e^{2 t}+c_5\right ) \sin \left (\sqrt {3} t\right )+c_4\right ) \end{align*}

✓ Sympy. Time used: 0.128 (sec). Leaf size: 63

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-64*x(t) + Derivative(x(t), (t, 6)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{5} e^{- 2 t} + C_{6} e^{2 t} + \left (C_{1} \sin {\left (\sqrt {3} t \right )} + C_{2} \cos {\left (\sqrt {3} t \right )}\right ) e^{- t} + \left (C_{3} \sin {\left (\sqrt {3} t \right )} + C_{4} \cos {\left (\sqrt {3} t \right )}\right ) e^{t} \]