90.17.9 problem 9

Internal problem ID [25271]
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 : 9
Date solved : Thursday, October 02, 2025 at 11:59:29 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+18 y^{\prime \prime }-27 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

ode:=diff(diff(diff(diff(y(t),t),t),t),t)+8*diff(diff(diff(y(t),t),t),t)+18*diff(diff(y(t),t),t)-27*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{4 t}+c_4 \,t^{2}+c_3 t +c_2 \right ) {\mathrm e}^{-3 t} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 32

ode=D[y[t],{t,4}]+8*D[y[t],{t,3}]+18*D[y[t],{t,2}]-27*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-3 t} \left (c_3 t^2+c_2 t+c_4 e^{4 t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.061 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-27*y(t) + 18*Derivative(y(t), (t, 2)) + 8*Derivative(y(t), (t, 3)) + Derivative(y(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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