Internal problem ID [2743]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 11.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\relax (5)}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$5)-6*diff(y(x),x$4)+9*diff(y(x),x$3)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+c_{2} x +c_{3} x^{2}+c_{4} {\mathrm e}^{3 x}+c_{5} {\mathrm e}^{3 x} x \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 35
DSolve[y'''''[x]-6*y''''[x]+9*y'''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{27} e^{3 x} (c_2 (x-1)+c_1)+x (c_5 x+c_4)+c_3 \\ \end{align*}