68.13.19 problem 36

Internal problem ID [17672]
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 : 36
Date solved : Thursday, October 02, 2025 at 02:26:58 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y&=0 \end{align*}

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

ode:=diff(diff(diff(diff(y(t),t),t),t),t)+2*diff(diff(y(t),t),t)+y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 26

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

\begin{align*} y(t)&\to (c_2 t+c_1) \cos (t)+(c_4 t+c_3) \sin (t) \end{align*}

✓ Sympy. Time used: 0.045 (sec). Leaf size: 19

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

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