82.24.2 problem Ex. 2

Internal problem ID [18789]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 65
Problem number : Ex. 2
Date solved : Thursday, March 13, 2025 at 12:59:01 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-m^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)-m^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = c_{1} {\mathrm e}^{-m x}+c_{2} {\mathrm e}^{m x} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 23

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

\[ y(x)\to c_1 e^{m x}+c_2 e^{-m x} \]

✓ Sympy. Time used: 0.077 (sec). Leaf size: 15

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

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