12.18.5 problem section 9.2, problem 5

Internal problem ID [2119]
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 5
Date solved : Tuesday, March 04, 2025 at 01:50:31 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+9 y^{\prime }+5 y&=0 \end{align*}

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

ode:=diff(diff(diff(y(x),x),x),x)+5*diff(diff(y(x),x),x)+9*diff(y(x),x)+5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} c_1 +c_2 \,{\mathrm e}^{-2 x} \sin \left (x \right )+c_3 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 28

ode=D[y[x],{x,3}]+5*D[y[x],{x,2}]+9*D[y[x],x]+5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (c_3 e^x+c_2 \cos (x)+c_1 \sin (x)\right ) \]

✓ Sympy. Time used: 0.196 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) + 9*Derivative(y(x), x) + 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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