74.13.12 problem 29

Internal problem ID [16378]
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 : 29
Date solved : Tuesday, January 28, 2025 at 09:07:20 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(diff(y(t),t$4)-16*y(t)=0,y(t), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{2 t}+{\mathrm e}^{-2 t} c_{2} +c_{3} \sin \left (2 t \right )+c_4 \cos \left (2 t \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 36

DSolve[D[y[t],{t,4}]-16*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_1 e^{2 t}+c_3 e^{-2 t}+c_2 \cos (2 t)+c_4 \sin (2 t) \]