65.6.6 problem 12.1 (vi)

Internal problem ID [13676]
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 : Wednesday, March 05, 2025 at 10:11:37 PM
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*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 10

ode:=diff(diff(theta(t),t),t)+4*theta(t) = 0; 
ic:=theta(0) = 0, D(theta)(0) = 10; 
dsolve([ode,ic],theta(t), singsol=all);
 

\[ \theta \left (t \right ) = 5 \sin \left (2 t \right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 11

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

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

✓ Sympy. Time used: 0.063 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
theta = Function("theta") 
ode = Eq(4*theta(t) + Derivative(theta(t), (t, 2)),0) 
ics = {theta(0): 0, Subs(Derivative(theta(t), t), t, 0): 10} 
dsolve(ode,func=theta(t),ics=ics)
 

\[ \theta {\left (t \right )} = 5 \sin {\left (2 t \right )} \]