18.12 problem section 9.2, problem 12

Internal problem ID [1476]

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 12.
ODE order: 4.
ODE degree: 1.

CAS Maple gives this as type [[_high_order, _missing_x]]

Solve \begin {gather*} \boxed {6 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+7 y^{\prime \prime }+5 y^{\prime }+y=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 25

dsolve(6*diff(y(x),x$4)+5*diff(y(x),x$3)+7*diff(y(x),x$2)+5*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 37

DSolve[6*y''''[x]+5*y'''[x]+7*y''[x]+5*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{-x/2} \left (c_3 e^{x/6}+c_4\right )+c_1 \cos (x)+c_2 \sin (x) \\ \end{align*}