Internal problem ID [1466]
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 2.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+8 y^{\prime \prime }-9 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 27
dsolve(diff(y(x),x$4)+8*diff(y(x),x$2)-9*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{x}+c_{3} \sin \left (3 x \right )+c_{4} \cos \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 34
DSolve[y''''[x]+8*y''[x]-9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 e^{-x}+c_4 e^x+c_1 \cos (3 x)+c_2 \sin (3 x) \\ \end{align*}