12.18.2 problem section 9.2, problem 2

Internal problem ID [2116]
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 2
Date solved : Tuesday, March 04, 2025 at 01:50:29 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }-9 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+8*diff(diff(y(x),x),x)-9*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} c_1 +c_2 \,{\mathrm e}^{-x}+c_3 \sin \left (3 x \right )+c_4 \cos \left (3 x \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 34

ode=D[y[x],{x,4}]+8*D[y[x],{x,2}]-9*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_3 e^{-x}+c_4 e^x+c_1 \cos (3 x)+c_2 \sin (3 x) \]

✓ Sympy. Time used: 0.084 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-9*y(x) + 8*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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