Internal problem ID [3253]
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]]
\[ \boxed {y^{\left (6\right )}-64 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 53
dsolve(diff(y(x),x$6)-64*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (\left (c_{4} {\mathrm e}^{3 x}+c_{6} {\mathrm e}^{x}\right ) \cos \left (\sqrt {3}\, x \right )+\left (c_{3} {\mathrm e}^{3 x}+c_{5} {\mathrm e}^{x}\right ) \sin \left (\sqrt {3}\, x \right )+{\mathrm e}^{4 x} c_{1} +c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 68
DSolve[y''''''[x]-64*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (c_1 e^{4 x}+e^x \left (c_2 e^{2 x}+c_3\right ) \cos \left (\sqrt {3} x\right )+e^x \left (c_6 e^{2 x}+c_5\right ) \sin \left (\sqrt {3} x\right )+c_4\right ) \]