67.12.18 problem 19.4 (b)

Internal problem ID [16657]
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 : 19.4 (b)
Date solved : Thursday, October 02, 2025 at 01:37:24 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+216 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 37

ode:=diff(diff(diff(y(x),x),x),x)+216*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-6 x}+c_2 \,{\mathrm e}^{3 x} \sin \left (3 \sqrt {3}\, x \right )+c_3 \,{\mathrm e}^{3 x} \cos \left (3 \sqrt {3}\, x \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 48

ode=D[y[x],{x,3}]+216*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-6 x} \left (c_3 e^{9 x} \cos \left (3 \sqrt {3} x\right )+c_2 e^{9 x} \sin \left (3 \sqrt {3} x\right )+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.079 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(216*y(x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} e^{- 6 x} + \left (C_{1} \sin {\left (3 \sqrt {3} x \right )} + C_{2} \cos {\left (3 \sqrt {3} x \right )}\right ) e^{3 x} \]