Internal problem ID [11708]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+\omega ^{2} y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (t \right ) = \frac {\sin \left (t \omega \right )}{\omega } \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 13
DSolve[{y''[t]+w^2*y[t]==0,{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {\sin (t w)}{w} \]