23.3.9 problem 7(i)

Internal problem ID [4150]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 7(i)
Date solved : Monday, January 27, 2025 at 08:40:03 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(x),x$6)+9*diff(y(x),x$4)+24*diff(y(x),x$2)+16*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_6 x +c_4 \right ) \cos \left (2 x \right )+\left (c_5 x +c_3 \right ) \sin \left (2 x \right )+c_{1} \sin \left (x \right )+c_{2} \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 40

DSolve[D[y[x],{x,6}]+9*D[y[x],{x,4}]+24*D[y[x],{x,2}]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (c_2 x+c_1) \cos (2 x)+c_6 \sin (x)+\cos (x) (2 (c_4 x+c_3) \sin (x)+c_5) \]