12.18.3 problem section 9.2, problem 3

Internal problem ID [2117]
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 3
Date solved : Monday, January 27, 2025 at 05:42:36 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+16 y^{\prime }-16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)-diff(y(x),x$2)+16*diff(y(x),x)-16*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} c_1 +\sin \left (4 x \right ) c_2 +c_3 \cos \left (4 x \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 26

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]+16*D[y[x],x]-16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 e^x+c_1 \cos (4 x)+c_2 \sin (4 x) \]