44.2.9 problem 9

Internal problem ID [6941]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 9
Date solved : Monday, January 27, 2025 at 02:37:38 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} x \left (\frac {\pi }{6}\right )&={\frac {1}{2}}\\ x^{\prime }\left (\frac {\pi }{6}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 16

dsolve([diff(x(t),t$2)+x(t)=0,x(1/6*Pi) = 1/2, D(x)(1/6*Pi) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\sin \left (t \right )}{4}+\frac {\sqrt {3}\, \cos \left (t \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 20

DSolve[{D[x[t],{t,2}]+x[t]==0,{x[Pi/6]==1/2,Derivative[1][x][Pi/6] == 0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{4} \left (\sin (t)+\sqrt {3} \cos (t)\right ) \]