68.13.22 problem 39

Internal problem ID [17675]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 39
Date solved : Thursday, October 02, 2025 at 02:26:59 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}+12 y^{\prime \prime \prime \prime }+48 y^{\prime \prime }+64 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

ode:=diff(diff(diff(diff(diff(diff(y(t),t),t),t),t),t),t)+12*diff(diff(diff(diff(y(t),t),t),t),t)+48*diff(diff(y(t),t),t)+64*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_6 \,t^{2}+c_4 t +c_2 \right ) \cos \left (2 t \right )+\sin \left (2 t \right ) \left (c_5 \,t^{2}+c_3 t +c_1 \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 40

ode=D[ y[t],{t,6}]+12*D[y[t],{t,4}]+48*D[y[t],{t,2}]+64*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to (t (c_3 t+c_2)+c_1) \cos (2 t)+(t (c_6 t+c_5)+c_4) \sin (2 t) \end{align*}

✓ Sympy. Time used: 0.075 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(64*y(t) + 48*Derivative(y(t), (t, 2)) + 12*Derivative(y(t), (t, 4)) + Derivative(y(t), (t, 6)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} + t \left (C_{2} + C_{3} t\right )\right ) \sin {\left (2 t \right )} + \left (C_{4} + t \left (C_{5} + C_{6} t\right )\right ) \cos {\left (2 t \right )} \]