14.8.9 problem 11

Internal problem ID [2564]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.2.1 Linear equations with constant coefficients (complex roots). Excercises page 144
Problem number : 11
Date solved : Tuesday, March 04, 2025 at 02:28:00 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+w^{2} y&=0 \end{align*}

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

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

\[ y = c_1 \sin \left (w t \right )+c_2 \cos \left (w t \right ) \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 20

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

\[ y(t)\to c_1 \cos (t w)+c_2 \sin (t w) \]

✓ Sympy. Time used: 0.095 (sec). Leaf size: 19

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

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