6.18.3 problem section 9.2, problem 3

Internal problem ID [2117]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 3
Date solved : Tuesday, September 30, 2025 at 05:24:12 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+16 y^{\prime }-16 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

\[ y = c_1 \,{\mathrm e}^{x}+c_2 \sin \left (4 x \right )+c_3 \cos \left (4 x \right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 26

ode=D[y[x],{x,3}]-D[y[x],{x,2}]+16*D[y[x],x]-16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3 e^x+c_1 \cos (4 x)+c_2 \sin (4 x) \end{align*}

✓ Sympy. Time used: 0.092 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-16*y(x) + 16*Derivative(y(x), x) - Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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