89.13.17 problem 17

Internal problem ID [24600]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 127
Problem number : 17
Date solved : Thursday, October 02, 2025 at 10:46:25 PM
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*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 33

ode:=diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x)+9*diff(diff(diff(diff(y(x),x),x),x),x)+24*diff(diff(y(x),x),x)+16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 40

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

\begin{align*} 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) \end{align*}

✓ Sympy. Time used: 0.070 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) + 24*Derivative(y(x), (x, 2)) + 9*Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 6)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{5} \sin {\left (x \right )} + C_{6} \cos {\left (x \right )} + \left (C_{1} + C_{2} x\right ) \sin {\left (2 x \right )} + \left (C_{3} + C_{4} x\right ) \cos {\left (2 x \right )} \]