Internal problem ID [14104]
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.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 y \left (t \right )\\ y^{\prime }\left (t \right )&=-4 x \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 4, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
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[{x'[t]==4*y[t],y'[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*}