10.20.5 problem 3 part 2

Internal problem ID [1461]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 9.2, Autonomous Systems and Stability. page 517
Problem number : 3 part 2
Date solved : Monday, January 27, 2025 at 04:57:40 AM
CAS classification : system_of_ODEs

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 16

DSolve[{D[x[t],t]==-0*x[t]-1*y[t],D[y[t],t]==1*x[t]+0*y[t]},{x[0]==0,y[0]==4},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

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