75.7.3 problem 4

Internal problem ID [19985]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter VI. Certain particular forms of equations. Exercises at page 74
Problem number : 4
Date solved : Thursday, October 02, 2025 at 05:04:47 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.044 (sec). Leaf size: 19

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

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