75.1.4 problem 2

Internal problem ID [19885]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter I. Introduction. Exercises at page 13
Problem number : 2
Date solved : Thursday, October 02, 2025 at 05:00:16 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

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

\[ y = c_1 \sin \left (m x \right )+c_2 \cos \left (m x \right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to c_1 \cos (m x)+c_2 \sin (m x) \end{align*}

✓ Sympy. Time used: 0.043 (sec). Leaf size: 19

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)
 

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