12.18.5 problem section 9.2, problem 5

Internal problem ID [2119]
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 5
Date solved : Monday, January 27, 2025 at 05:42:37 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+9 y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$3)+5*diff(y(x),x$2)+9*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x} c_1 +c_2 \,{\mathrm e}^{-2 x} \sin \left (x \right )+c_3 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 28

DSolve[D[y[x],{x,3}]+5*D[y[x],{x,2}]+9*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (c_3 e^x+c_2 \cos (x)+c_1 \sin (x)\right ) \]