89.14.6 problem 6

Internal problem ID [24610]
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 128
Problem number : 6
Date solved : Thursday, October 02, 2025 at 10:46:29 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-16 y^{\prime }-16 y&=0 \end{align*}

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

ode:=diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)-16*diff(y(x),x)-16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_3 \,{\mathrm e}^{8 x}+c_2 \,{\mathrm e}^{3 x}+c_1 \right ) {\mathrm e}^{-4 x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 30

ode=D[y[x],{x,3}]+D[y[x],{x,2}]-16*D[y[x],{x,1}]-16*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-4 x} \left (c_2 e^{3 x}+c_3 e^{8 x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-16*y(x) - 16*Derivative(y(x), x) + Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 4 x} + C_{2} e^{- x} + C_{3} e^{4 x} \]