89.13.5 problem 5

Internal problem ID [24588]
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 127
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:46:18 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\[ y = c_1 \,{\mathrm e}^{-3 x}+c_2 \,{\mathrm e}^{3 x} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to e^{-3 x} \left (c_1 e^{6 x}+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.030 (sec). Leaf size: 15

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

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