Internal problem ID [811]
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.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=-y \relax (t )\\ y^{\prime }\relax (t )&=x \relax (t ) \end {align*}
With initial conditions \[ [x \relax (0) = 0, y \relax (0) = 4] \]
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 16
dsolve([diff(x(t),t) = -y(t), diff(y(t),t) = x(t), x(0) = 0, y(0) = 4],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -4 \sin \relax (t ) \] \[ y \relax (t ) = 4 \cos \relax (t ) \]
✓ 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]==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*}