Internal problem ID [810]
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 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 4, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve([diff(x(t),t) = -y(t), diff(y(t),t) = x(t), x(0) = 4, y(0) = 0], singsol=all)
\begin{align*} x \left (t \right ) &= 4 \cos \left (t \right ) \\ y \left (t \right ) &= 4 \sin \left (t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 16
DSolve[{x'[t]==-0*x[t]-1*y[t],y'[t]==1*x[t]+0*y[t]},{x[0]==4,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 4 \cos (t) \\ y(t)\to 4 \sin (t) \\ \end{align*}