18.8 problem section 9.2, problem 8

Internal problem ID [1472]

Book: Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number: section 9.2, problem 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(x),x$4)+diff(y(x),x$2)=0,y(x), singsol=all)
 

\[ y \relax (x ) = c_{1}+c_{2} x +c_{3} \sin \relax (x )+c_{4} \cos \relax (x ) \]

Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 24

DSolve[y''''[x]+y''[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_4 x-c_1 \cos (x)-c_2 \sin (x)+c_3 \\ \end{align*}