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 : Monday, January 27, 2025 at 04:57:42 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

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

dsolve(diff(y(t),t$4)+diff(y(t),t$2)=0,y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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