Internal problem ID [827]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 4.2, Higher order linear differential equations. Constant coefficients. page
180
Problem number: 13.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\relax (6)}-y^{\prime \prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 27
dsolve(diff(y(x),x$6)-diff(y(x),x$2)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+c_{2} x +c_{3} {\mathrm e}^{-x}+c_{4} {\mathrm e}^{x}+c_{5} \sin \relax (x )+c_{6} \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 38
DSolve[y''''''[x]-y''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x+c_3 e^{-x}+c_6 x-c_2 \cos (x)-c_4 \sin (x)+c_5 \\ \end{align*}