68.13.16 problem 33

Internal problem ID [17669]
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 : 33
Date solved : Thursday, October 02, 2025 at 02:26:57 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=diff(diff(diff(diff(diff(y(t),t),t),t),t),t)+4*diff(diff(diff(diff(y(t),t),t),t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 +c_2 t +c_3 \,t^{2}+c_4 \,t^{3}+c_5 \,{\mathrm e}^{-4 t} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 33

ode=D[ y[t],{t,5}]+4*D[y[t],{t,4}]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{256} c_1 e^{-4 t}+t (t (c_5 t+c_4)+c_3)+c_2 \end{align*}

✓ Sympy. Time used: 0.055 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*Derivative(y(t), (t, 4)) + Derivative(y(t), (t, 5)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} + C_{2} t + C_{3} t^{2} + C_{4} t^{3} + C_{5} e^{- 4 t} \]