Internal problem ID [14640]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+16 y^{\prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(t),t$4)+16*diff(y(t),t$2)=0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} +t c_{2} +c_{3} \sin \left (4 t \right )+c_{4} \cos \left (4 t \right ) \]
✓ Solution by Mathematica
Time used: 0.17 (sec). Leaf size: 32
DSolve[y''''[t]+16*y''[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to c_4 t-\frac {1}{16} c_1 \cos (4 t)-\frac {1}{16} c_2 \sin (4 t)+c_3 \]