12.18.2 problem section 9.2, problem 2

Internal problem ID [2116]
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 2
Date solved : Monday, January 27, 2025 at 05:42:36 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }-9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(diff(y(x),x$4)+8*diff(y(x),x$2)-9*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} c_1 +c_2 \,{\mathrm e}^{-x}+c_3 \sin \left (3 x \right )+c_4 \cos \left (3 x \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 34

DSolve[D[y[x],{x,4}]+8*D[y[x],{x,2}]-9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 e^{-x}+c_4 e^x+c_1 \cos (3 x)+c_2 \sin (3 x) \]