44.2.8 problem 8

Internal problem ID [6940]
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 : 8
Date solved : Monday, January 27, 2025 at 02:37:35 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 }{2}\right )&=0\\ x^{\prime }\left (\frac {\pi }{2}\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 8

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

\[ x \left (t \right ) = -\cos \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 9

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

\[ x(t)\to -\cos (t) \]