Ryan Smith

I have yet to meet a human who enjoys plotting vector fields. However, my computer loves them. With a super swell package from http://www.appliedsymbols.com/ you can teach your machine to plot slope fields.

Now, without stating or proving the Picard–Lindelöf theorem (these guys showed that for an initial value problem there exists a unique solution) we will take a look at a solution of an Ordinary Differential Equation via it’s slope fields.

consider:

This seems like a tricky ODE. However we can observe some of it’s strange behavior by plotting the slopes at different points in the chosen interval. This is how we do it in mathematica.

So go grab the DE package for mathematica and play around. We will come back to this interesting equation later…….