68.13.4 problem 21

Internal problem ID [17657]
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 : 21
Date solved : Thursday, October 02, 2025 at 02:26:54 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+16 y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(diff(diff(y(t),t),t),t),t)+16*diff(diff(y(t),t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 +c_2 t +c_3 \sin \left (4 t \right )+c_4 \cos \left (4 t \right ) \]

✓ Mathematica. Time used: 60.022 (sec). Leaf size: 44

ode=D[y[t],{t,4}]+16*D[y[t],{t,2}]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \int _1^t\int _1^{K[2]}(c_1 \cos (4 K[1])+c_2 \sin (4 K[1]))dK[1]dK[2]+c_4 t+c_3 \end{align*}

✓ Sympy. Time used: 0.031 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(16*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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