74.1.60 problem 82

Internal problem ID [15840]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 82
Date solved : Tuesday, January 28, 2025 at 08:09:15 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=4 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-4 x \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 4\\ y \left (0\right ) = 0 \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 19

dsolve([diff(x(t),t) = 4*y(t), diff(y(t),t) = -4*x(t), x(0) = 4, y(0) = 0], singsol=all)
 

\begin{align*} x \left (t \right ) &= 4 \cos \left (4 t \right ) \\ y \left (t \right ) &= -4 \sin \left (4 t \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 20

DSolve[{D[x[t],t]==4*y[t],D[y[t],t]==-4*x[t]},{x[0]==4,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to 4 \cos (4 t) \\ y(t)\to -4 \sin (4 t) \\ \end{align*}