7.29 problem Exercise 20.30, page 220

Internal problem ID [4092]

Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number: Exercise 20.30, page 220.
ODE order: 5.
ODE degree: 1.

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

Solve \begin {gather*} \boxed {y^{\relax (5)}+2 y^{\prime \prime \prime }+y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 24

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

\[ y \relax (x ) = c_{1}+c_{2} \sin \relax (x )+c_{3} \cos \relax (x )+c_{4} \sin \relax (x ) x +c_{5} \cos \relax (x ) x \]

Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 35

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

\begin{align*} y(x)\to (-c_4 x+c_2-c_3) \cos (x)+(c_2 x+c_1+c_4) \sin (x)+c_5 \\ \end{align*}