68.14.2 problem 2

Internal problem ID [17694]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number : 2
Date solved : Thursday, October 02, 2025 at 02:27:07 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-16 y&=1 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 30

ode:=diff(diff(diff(diff(y(t),t),t),t),t)-16*y(t) = 1; 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {1}{16}+c_1 \cos \left (2 t \right )+c_2 \,{\mathrm e}^{-2 t}+c_3 \,{\mathrm e}^{2 t}+c_4 \sin \left (2 t \right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 39

ode=D[y[t],{t,4}]-16*y[t]==1; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to c_1 e^{2 t}+c_3 e^{-2 t}+c_2 \cos (2 t)+c_4 \sin (2 t)-\frac {1}{16} \end{align*}

✓ Sympy. Time used: 0.061 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-16*y(t) + Derivative(y(t), (t, 4)) - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 2 t} + C_{2} e^{2 t} + C_{3} \sin {\left (2 t \right )} + C_{4} \cos {\left (2 t \right )} - \frac {1}{16} \]