28.2.2 problem 2

Internal problem ID [4445]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 2
Date solved : Tuesday, March 04, 2025 at 06:44:16 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

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

\[ y \left (x \right ) = {\mathrm e}^{-x} c_{1} +\sin \left (3 x \right ) c_{2} +c_3 \cos \left (3 x \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 28

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

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

✓ Sympy. Time used: 0.160 (sec). Leaf size: 20

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

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