74.13.20 problem 37

Internal problem ID [16386]
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 : 37
Date solved : Tuesday, January 28, 2025 at 09:07:23 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 25

dsolve(diff(y(t),t$4)+8*diff(y(t),t$2)+16*y(t)=0,y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[D[y[t],{t,4}]+8*D[y[t],{t,2}]+16*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to (c_2 t+c_1) \cos (2 t)+(c_4 t+c_3) \sin (2 t) \]