Internal problem ID [814]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 4.1, Higher order linear differential equations. General theory. page 173
Problem number: 8.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 17
dsolve(diff(y(t),t$4)+diff(y(t),t$2)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1}+c_{2} t +c_{3} \sin \relax (t )+c_{4} \cos \relax (t ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 24
DSolve[y''''[t]+y''[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_4 t-c_1 \cos (t)-c_2 \sin (t)+c_3 \\ \end{align*}