It is very easy to use Mathematica to make stream plots for differential equations.

## Stream plots for a single equation

Consider the example

Points on a solution curve to this equation will take the form . Thus the slope will look like

.

Using the differential equation, we see that

Thus this is what we want to plot. The Mathematica code for this is the following:

```
```StreamPlot[{1,(y-y^3) Cos[t]}, {t,0,5},{y,-2,2}]

The output is this:

Notice the following:

- The command
`{1,(y-y^3) Cos[t]}`

gives the slope to be plotted at each point. - The command
`{t,0,5}`

gives the range of values. - The command
`{y,-2,2}`

gives the range of values.

Notice also that it is easy to see the equilibrium solutions on the picture – how cool is that!

## Stream plots for systems

For a system of the form

we can make a stream plot on the domain , using

```
```StreamPlot[{f(x,y),g(x,y)},{x,a,b},{y,c,d}]

For example, the stream plot for the system

is generated using the code

```
```StreamPlot[{x(1-x)+Sin[y], y^2+x/Exp[y]},{x,-2,2},{y,-3,3}]

The result is

Reblogged this on Mario A. G. Meza.