7.8.2 problem 2

Internal problem ID [216]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 2
Date solved : Tuesday, March 04, 2025 at 11:04:56 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=15 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)-9*y(x) = 0; 
ic:=y(0) = -1, D(y)(0) = 15; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -3 \,{\mathrm e}^{-3 x}+2 \,{\mathrm e}^{3 x} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 20

ode=D[y[x],{x,2}]-9*y[x] == 0; 
ic={y[0]==-1,Derivative[1][y][0] ==15}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x} \left (2 e^{6 x}-3\right ) \]

✓ Sympy. Time used: 0.079 (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 = {y(0): -1, Subs(Derivative(y(x), x), x, 0): 15} 
dsolve(ode,func=y(x),ics=ics)
 

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