74.13.4 problem 21

Internal problem ID [16370]
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 : 21
Date solved : Tuesday, January 28, 2025 at 09:07:17 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

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

dsolve(diff(y(t),t$4)+16*diff(y(t),t$2)=0,y(t), singsol=all)
 

\[ y = c_{1} +c_{2} t +c_{3} \sin \left (4 t \right )+c_4 \cos \left (4 t \right ) \]

✓ Solution by Mathematica

Time used: 60.034 (sec). Leaf size: 44

DSolve[D[y[t],{t,4}]+16*D[y[t],{t,2}]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^t\int _1^{K[2]}(c_1 \cos (4 K[1])+c_2 \sin (4 K[1]))dK[1]dK[2]+c_4 t+c_3 \]