Internal problem ID [2739]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 7.
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 }+18 y^{\prime \prime }+81 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$4)+18*diff(y(x),x$2)+81*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (3 x \right )+c_{2} \cos \left (3 x \right )+c_{3} \sin \left (3 x \right ) x +c_{4} \cos \left (3 x \right ) x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 30
DSolve[y''''[x]+18*y''[x]+81*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (c_2 x+c_1) \cos (3 x)+(c_4 x+c_3) \sin (3 x) \\ \end{align*}