Internal problem ID [2744]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 12.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\relax (6)}-64 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 61
dsolve(diff(y(x),x$6)-64*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{x} \sin \left (\sqrt {3}\, x \right )+c_{4} {\mathrm e}^{x} \cos \left (\sqrt {3}\, x \right )+c_{5} {\mathrm e}^{-x} \sin \left (\sqrt {3}\, x \right )+c_{6} {\mathrm e}^{-x} \cos \left (\sqrt {3}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 67
DSolve[y''''''[x]-64*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (c_1 e^{4 x}+e^x \left (\left (c_2 e^{2 x}+c_3\right ) \cos \left (\sqrt {3} x\right )+\left (c_6 e^{2 x}+c_5\right ) \sin \left (\sqrt {3} x\right )\right )+c_4\right ) \\ \end{align*}