Internal problem ID [5111]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page
181
Problem number: Example 3.37.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\relax (5)}-\frac {y^{\prime \prime \prime \prime }}{t}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 24
dsolve(diff(y(t),t$5)-1/t*diff(y(t),t$4)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{5} t^{5}+c_{3} t^{3}+t^{2} c_{2}+c_{4} t +c_{1} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 33
DSolve[y'''''[t]-1/t*y''''[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {c_1 t^5}{120}+c_5 t^3+c_4 t^2+c_3 t+c_2 \\ \end{align*}