68.13.13 problem 30

Internal problem ID [17666]
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 : 30
Date solved : Thursday, October 02, 2025 at 02:26:56 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }-y^{\prime \prime }+54 y^{\prime }-72 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

ode:=diff(diff(diff(diff(y(t),t),t),t),t)-6*diff(diff(diff(y(t),t),t),t)-diff(diff(y(t),t),t)+54*diff(y(t),t)-72*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{7 t}+c_4 \,{\mathrm e}^{6 t}+c_2 \,{\mathrm e}^{5 t}+c_3 \right ) {\mathrm e}^{-3 t} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 36

ode=D[y[t],{t,4}]-6*D[ y[t],{t,3}]-D[y[t],{t,2}]+54*D[y[t],t]-72*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-3 t} \left (e^{5 t} \left (e^t \left (c_4 e^t+c_3\right )+c_2\right )+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.121 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-72*y(t) + 54*Derivative(y(t), t) - Derivative(y(t), (t, 2)) - 6*Derivative(y(t), (t, 3)) + Derivative(y(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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