74.14.2 problem 2

Internal problem ID [16407]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 09:07:36 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-16 y&=1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

dsolve(diff(y(t),t$4)-16*y(t)=1,y(t), singsol=all)
 

\[ y = -\frac {1}{16}+\cos \left (2 t \right ) c_{1} +{\mathrm e}^{-2 t} c_{2} +c_{3} {\mathrm e}^{2 t}+c_4 \sin \left (2 t \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 39

DSolve[D[y[t],{t,4}]-16*y[t]==1,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_1 e^{2 t}+c_3 e^{-2 t}+c_2 \cos (2 t)+c_4 \sin (2 t)-\frac {1}{16} \]