# example5: Example ODE System Number Five In phaseR: Phase Plane Analysis of One and Two Dimensional Autonomous ODE Systems

## Description

The derivative function of an example two dimensional autonomous ODE system.

## Usage

 `1` ```example5(t, y, parameters) ```

## Arguments

 `t` Value of t, the independent variable, to evaluate the derivative at. Should be a single number. `y` Values of x and y, the dependent variables, to evaluate the derivative at. Should be a vector of length 2. `parameters` Values of the parameters of the system. Not required here.

## Details

Evaluates the derivatives of the following coupled ODE system at the point (t,x,y):

dx/dt = 2*x + y, dy/dt = 2*x - y.

Format is designed to be compatible with ode from the deSolve package.

## Value

Returns a list dy containing the values of the two derivatives at (t, x, y).

## Author(s)

Michael J. Grayling

`ode`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```# Plot the velocity field, nullclines and several trajectories. example5.flowField <- flowField(example5, x.lim = c(-3, 3), y.lim = c(-3, 3), points = 19, add = FALSE) y0 <- matrix(c(1, 0, -1, 0, 2, 2, -2, 2, 0, 3, 0, -3), ncol = 2, nrow = 6, byrow = TRUE) example5.nullclines <- nullclines(example5, x.lim = c(-3, 3), y.lim = c(-3, 3)) example5.trajectory <- trajectory(example5, y0 = y0, t.end = 10) # Plot x and y against t. example5.numericalSolution <- numericalSolution(example5, y0 = c(0, 3), t.end = 3) # Determine the stability of the equilibrium point. example5.stability <- stability(example5, y.star = c(0, 0)) ```