2.7.2 problem 2

Internal problem ID [808]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 04:15:33 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: 0.051 (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,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.009 (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]
 

\begin{align*} y(x)&\to e^{-3 x} \left (2 e^{6 x}-3\right ) \end{align*}

✓ Sympy. Time used: 0.045 (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)
 

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