65.6.6 problem 12.1 (vi)

Internal problem ID [13755]
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)
Date solved : Tuesday, January 28, 2025 at 06:01:58 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} \theta ^{\prime \prime }+4 \theta &=0 \end{align*}

With initial conditions

\begin{align*} \theta \left (0\right )&=0\\ \theta ^{\prime }\left (0\right )&=10 \end{align*}

✓ Solution by Maple

Time used: 0.009 (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: 0.013 (sec). Leaf size: 11

DSolve[{D[ \[Theta][t], {t,2}]+4*\[Theta][t]==0,{\[Theta][0]==0,Derivative[1][ \[Theta]][0] ==10}},\[Theta][t],t,IncludeSingularSolutions -> True]
 

\[ \theta (t)\to 5 \sin (2 t) \]