12.18.7 problem section 9.2, problem 7

Internal problem ID [2121]
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 7
Date solved : Tuesday, March 04, 2025 at 01:50:32 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 27 y^{\prime \prime \prime }+27 y^{\prime \prime }+9 y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=27*diff(diff(diff(y(x),x),x),x)+27*diff(diff(y(x),x),x)+9*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {x}{3}} \left (c_3 \,x^{2}+c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 25

ode=27*D[y[x],{x,3}]+27*D[y[x],{x,2}]+9*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.167 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + 9*Derivative(y(x), x) + 27*Derivative(y(x), (x, 2)) + 27*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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