Internal problem ID [2742]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 10.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+5 y^{\prime \prime }+5 y^{\prime }-6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(diff(y(x),x$4)-5*diff(y(x),x$3)+5*diff(y(x),x$2)+5*diff(y(x),x)-6*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{x}+c_{4} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 36
DSolve[y''''[x]-5*y'''[x]+5*y''[x]+5*y'[x]-6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x}+c_2 e^x+c_3 e^{2 x}+c_4 e^{3 x} \\ \end{align*}