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 : Monday, January 27, 2025 at 06:00:46 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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