74.19.5 problem 5

Internal problem ID [16627]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 5. Applications of Higher Order Equations. Exercises 5.1, page 232
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 09:13:15 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} x \left (0\right )&=3\\ x^{\prime }\left (0\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 13

dsolve([diff(x(t),t$2)+x(t)=0,x(0) = 3, D(x)(0) = -4],x(t), singsol=all)
 

\[ x \left (t \right ) = -4 \sin \left (t \right )+3 \cos \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 14

DSolve[{D[x[t],{t,2}]+x[t]==0,{x[0]==3,Derivative[1][x][0 ]==-4}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 3 \cos (t)-4 \sin (t) \]