67.12.6 problem 19.1 (f)

Internal problem ID [16645]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.1 (f)
Date solved : Thursday, October 02, 2025 at 01:37:20 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)+18*diff(diff(diff(y(x),x),x),x)+81*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_5 x +c_3 \right ) \cos \left (3 x \right )+\left (c_4 x +c_2 \right ) \sin \left (3 x \right )+c_1 \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 44

ode=D[y[x],{x,5}]+18*D[y[x],{x,3}]+81*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^x(\cos (3 K[1]) (c_1+c_2 K[1])+(c_3+c_4 K[1]) \sin (3 K[1]))dK[1]+c_5 \end{align*}

✓ Sympy. Time used: 0.113 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(81*Derivative(y(x), x) + 18*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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