68.13.11 problem 28

Internal problem ID [17664]
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 : 28
Date solved : Thursday, October 02, 2025 at 02:26:56 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-9 y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=diff(diff(diff(diff(y(t),t),t),t),t)-9*diff(diff(y(t),t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 +c_2 t +c_3 \,{\mathrm e}^{-3 t}+c_4 \,{\mathrm e}^{3 t} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 32

ode=D[y[t],{t,4}]-9*D[y[t],{t,2}]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{9} e^{-3 t} \left (c_1 e^{6 t}+c_2\right )+c_4 t+c_3 \end{align*}

✓ Sympy. Time used: 0.047 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-9*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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