74.13.22 problem 39

Internal problem ID [16388]
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 : 39
Date solved : Tuesday, January 28, 2025 at 09:07:24 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}+12 y^{\prime \prime \prime \prime }+48 y^{\prime \prime }+64 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 35

dsolve(diff(y(t),t$6)+12*diff(y(t),t$4)+48*diff(y(t),t$2)+64*y(t)=0,y(t), singsol=all)
 

\[ y = \left (c_6 \,t^{2}+t c_4 +c_{2} \right ) \cos \left (2 t \right )+\sin \left (2 t \right ) \left (t^{2} c_5 +c_{3} t +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 40

DSolve[D[ y[t],{t,6}]+12*D[y[t],{t,4}]+48*D[y[t],{t,2}]+64*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to (t (c_3 t+c_2)+c_1) \cos (2 t)+(t (c_6 t+c_5)+c_4) \sin (2 t) \]