72.15.5 problem 5

Internal problem ID [19647]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 22. Higher Order Linear Equations. Coupled Harmonic Oscillators. Problems at page 160
Problem number : 5
Date solved : Thursday, October 02, 2025 at 04:41:04 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)+3*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.093 (sec). Leaf size: 14

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

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