Internal problem ID [12019]
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 (vi).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {\theta ^{\prime \prime }+4 \theta =0} \] With initial conditions \begin {align*} [\theta \left (0\right ) = 0, \theta ^{\prime }\left (0\right ) = 10] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 10
dsolve([diff(theta(t),t$2)+4*theta(t)=0,theta(0) = 0, D(theta)(0) = 10],theta(t), singsol=all)
\[ \theta \left (t \right ) = 5 \sin \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 11
DSolve[{\[Theta]''[t]+4*\[Theta][t]==0,{\[Theta][0]==0,\[Theta]'[0]==10}},\[Theta][t],t,IncludeSingularSolutions -> True]
\[ \theta (t)\to 5 \sin (2 t) \]