90.17.3 problem 3

Internal problem ID [25265]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 4. Linear Constant Coefficient Differential Equations. Exercises at page 291
Problem number : 3
Date solved : Thursday, October 02, 2025 at 11:59:27 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=diff(diff(diff(diff(y(t),t),t),t),t)-y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 30

ode=D[y[t],{t,4}]-y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.046 (sec). Leaf size: 22

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

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