73.11.12 problem 17.2 (f)

Internal problem ID [15255]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 17. Second order Homogeneous equations with constant coefficients. Additional exercises page 334
Problem number : 17.2 (f)
Date solved : Monday, March 31, 2025 at 01:32:34 PM
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 )&=3\\ y^{\prime }\left (0\right )&=-3 \end{align*}

✓ Maple. Time used: 0.043 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)-9*y(x) = 0; 
ic:=y(0) = 3, D(y)(0) = -3; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 18

ode=D[y[x],{x,2}]-9*y[x]==0; 
ic={y[0]==3,Derivative[1][y][0] ==-3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.083 (sec). Leaf size: 14

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

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