Internal problem ID [828]
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: 14.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\relax (5)}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 24
dsolve(diff(y(x),x$5)-3*diff(y(x),x$4)+3*diff(y(x),x$3)-3*diff(y(x),x$2)+2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{x}+c_{4} \sin \relax (x )+c_{5} \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 36
DSolve[y'''''[x]-3*y''''[x]+3*y'''[x]-3*y''[x]+2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 e^x+\frac {1}{2} c_4 e^{2 x}-c_2 \cos (x)+c_1 \sin (x)+c_5 \\ \end{align*}