18.14 problem section 9.2, problem 14

Internal problem ID [1478]

Book: Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number: section 9.2, problem 14.
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 }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y=0} \end {gather*}

Solution by Maple

Time used: 0.005 (sec). Leaf size: 26

dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+7*diff(y(x),x$2)-6*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} x \,{\mathrm e}^{x}+c_{3} \sin \relax (x ) {\mathrm e}^{x}+c_{4} \cos \relax (x ) {\mathrm e}^{x} \]

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 26

DSolve[y''''[x]-4*y'''[x]+7*y''[x]-6*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^x (c_4 x+c_2 \cos (x)+c_1 \sin (x)+c_3) \\ \end{align*}