89.12.4 problem 4

Internal problem ID [24558]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 121
Problem number : 4
Date solved : Thursday, October 02, 2025 at 10:46:06 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime \prime }+6 y^{\prime \prime }+y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=9*diff(diff(diff(y(x),x),x),x)+6*diff(diff(y(x),x),x)+diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 26

ode=9*D[y[x],{x,3}]+6*D[y[x],{x,2}] +D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3-3 e^{-x/3} (c_2 (x+3)+c_1) \end{align*}

✓ Sympy. Time used: 0.080 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + 6*Derivative(y(x), (x, 2)) + 9*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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