11.1.3 problem 8

Internal problem ID [1464]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 4.1, Higher order linear differential equations. General theory. page 173
Problem number : 8
Date solved : Saturday, March 29, 2025 at 10:55:51 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.077 (sec). Leaf size: 24

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

\[ y(t)\to c_4 t-c_1 \cos (t)-c_2 \sin (t)+c_3 \]

✓ Sympy. Time used: 0.056 (sec). Leaf size: 17

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

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