Internal problem ID [826]
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: 12.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\relax (6)}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 43
dsolve(diff(y(x),x$6)-3*diff(y(x),x$4)+3*diff(y(x),x$2)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{-x} x +c_{3} {\mathrm e}^{-x} x^{2}+c_{4} {\mathrm e}^{x}+c_{5} {\mathrm e}^{x} x +c_{6} {\mathrm e}^{x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 41
DSolve[y''''''[x]-3*y''''[x]+3*y''[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (x (c_3 x+c_2)+e^{2 x} (x (c_6 x+c_5)+c_4)+c_1\right ) \\ \end{align*}