Internal problem ID [1467]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+16 y^{\prime }-16 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \relax (x ) = {\mathrm e}^{x} c_{1}+c_{2} \sin \left (4 x \right )+c_{3} \cos \left (4 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 26
DSolve[y'''[x]-y''[x]+16*y'[x]-16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 e^x+c_1 \cos (4 x)+c_2 \sin (4 x) \\ \end{align*}