32.7.29 problem Exercise 20.30, page 220

Internal problem ID [5944]
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
Date solved : Monday, January 27, 2025 at 01:27:53 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

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

\[ y \left (x \right ) = \left (c_5 x +c_3 \right ) \cos \left (x \right )+\left (c_4 x +c_{2} \right ) \sin \left (x \right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 35

DSolve[D[y[x],{x,5}]+2*D[y[x],{x,3}]+D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (-c_4 x+c_2-c_3) \cos (x)+(c_2 x+c_1+c_4) \sin (x)+c_5 \]