Internal problem ID [1469]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+5 y^{\prime \prime }+9 y^{\prime }+5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{-2 x} \sin \relax (x )+c_{3} {\mathrm e}^{-2 x} \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 28
DSolve[y'''[x]+5*y''[x]+9*y'[x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (c_3 e^x+c_2 \cos (x)+c_1 \sin (x)\right ) \\ \end{align*}