Internal problem ID [14658]
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.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (6\right )}+12 y^{\prime \prime \prime \prime }+48 y^{\prime \prime }+64 y=0} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (t \right ) = \left (c_{6} t^{2}+t c_{4} +c_{2} \right ) \cos \left (2 t \right )+\sin \left (2 t \right ) \left (c_{5} t^{2}+c_{3} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 40
DSolve[y''''''[t]+12*y''''[t]+48*y''[t]+64*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to (t (c_3 t+c_2)+c_1) \cos (2 t)+(t (c_6 t+c_5)+c_4) \sin (2 t) \]