65.6.15 problem 12.1 (xv)

Internal problem ID [13764]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number : 12.1 (xv)
Date solved : Tuesday, January 28, 2025 at 06:02:20 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 12

dsolve([diff(y(t),t$2)+omega^2*y(t)=0,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
 

\[ y = \frac {\sin \left (\omega t \right )}{\omega } \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 13

DSolve[{D[y[t],{t,2}]+w^2*y[t]==0,{y[0]==0,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\sin (t w)}{w} \]