86.6.1 problem 1

Internal problem ID [23134]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5b at page 77
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:23:15 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+36 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=5 \\ x \left (\frac {\pi }{12}\right )&=7 \\ \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 17

ode:=diff(diff(x(t),t),t)+36*x(t) = 0; 
ic:=[x(0) = 5, x(1/12*Pi) = 7]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = 7 \sin \left (6 t \right )+5 \cos \left (6 t \right ) \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 18

ode=D[x[t],{t,2}]+36*x[t]==0; 
ic={x[0]==5,x[Pi/12]==7}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to 7 \sin (6 t)+5 \cos (6 t) \end{align*}

✓ Sympy. Time used: 0.034 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(36*x(t) + Derivative(x(t), (t, 2)),0) 
ics = {x(0): 5, x(pi/12): 7} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = 7 \sin {\left (6 t \right )} + 5 \cos {\left (6 t \right )} \]