90.18.4 problem 8

Internal problem ID [25276]
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 299
Problem number : 8
Date solved : Thursday, October 02, 2025 at 11:59:31 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{t}+{\mathrm e}^{-t} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 41

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

\[ y = \frac {{\mathrm e}^{-t} \left (-2 \ln \left ({\mathrm e}^{t}\right )+8 c_4 -3\right )}{8}+\frac {\left (8 c_2 +2 t -3\right ) {\mathrm e}^{t}}{8}+c_1 \cos \left (t \right )+c_3 \sin \left (t \right ) \]

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 65

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

\begin{align*} y(t)&\to \frac {1}{8} e^{-t} \left (2 e^{2 t} t-2 t-3 e^{2 t}+8 c_1 e^{2 t}+8 c_2 e^t \cos (t)+8 c_4 e^t \sin (t)-3+8 c_3\right ) \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 29

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

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