Internal problem ID [14653]
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: 34.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}+4 y^{\prime \prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(t),t$5)+4*diff(y(t),t$3)=0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} +t c_{2} +c_{3} t^{2}+c_{4} \sin \left (2 t \right )+c_{5} \cos \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.204 (sec). Leaf size: 38
DSolve[y'''''[t]+4*y'''[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to c_5 t^2+c_4 t+\frac {1}{8} c_2 \cos (2 t)-\frac {1}{8} c_1 \sin (2 t)+c_3 \]