28.2.2 problem 2

Internal problem ID [4445]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 2
Date solved : Monday, January 27, 2025 at 09:17:47 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$3)+diff(y(x),x$2)+9*diff(y(x),x)+9*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-x} c_{1} +\sin \left (3 x \right ) c_{2} +c_3 \cos \left (3 x \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 28

DSolve[D[y[x],{x,3}]+D[y[x],{x,2}]+9*D[y[x],x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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