68.13.17 problem 34

Internal problem ID [17670]
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 : 34
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 }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

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

\[ y = c_1 +c_2 t +c_3 \,t^{2}+c_4 \sin \left (2 t \right )+c_5 \cos \left (2 t \right ) \]

✓ Mathematica. Time used: 60.025 (sec). Leaf size: 57

ode=D[ y[t],{t,5}]+4*D[ y[t],{t,3}]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \int _1^t\int _1^{K[3]}\int _1^{K[2]}(c_1 \cos (2 K[1])+c_2 \sin (2 K[1]))dK[1]dK[2]dK[3]+t (c_5 t+c_4)+c_3 \end{align*}

✓ Sympy. Time used: 0.035 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*Derivative(y(t), (t, 3)) + Derivative(y(t), (t, 5)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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