18.9 problem section 9.2, problem 9

Internal problem ID [1473]

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 9.
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 }-16 y=0} \end {gather*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 29

dsolve(diff(y(x),x$4)-16*y(x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = {\mathrm e}^{-2 x} c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} \sin \left (2 x \right )+c_{4} \cos \left (2 x \right ) \]

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 36

DSolve[y''''[x]-16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{2 x}+c_3 e^{-2 x}+c_2 \cos (2 x)+c_4 \sin (2 x) \\ \end{align*}