44.2.7 problem 7

Internal problem ID [6939]
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 : 7
Date solved : Monday, January 27, 2025 at 02:37:31 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} x \left (0\right )&=-1\\ x^{\prime }\left (0\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 13

dsolve([diff(x(t),t$2)+x(t)=0,x(0) = -1, D(x)(0) = 8],x(t), singsol=all)
 

\[ x \left (t \right ) = 8 \sin \left (t \right )-\cos \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 14

DSolve[{D[x[t],{t,2}]+x[t]==0,{x[0]==-1,Derivative[1][x][0] == 8}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 8 \sin (t)-\cos (t) \]