15.18.3 problem 3

Internal problem ID [3246]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 3
Date solved : Tuesday, March 04, 2025 at 04:09:03 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+k^{2} x&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 17

ode:=diff(diff(x(t),t),t)+k^2*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_{1} \sin \left (k t \right )+c_2 \cos \left (k t \right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 20

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

\[ x(t)\to c_1 \cos (k t)+c_2 \sin (k t) \]

✓ Sympy. Time used: 0.079 (sec). Leaf size: 19

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

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