Putting the solutions and the slope fields together

Often, you will want to plot the solution curves for different initial conditions along with the slope field together on one graph.  You can do that by combining the solution graphing we did above with the slope fields.

Because I picked a pretty nasty equation, DSolve doesn't work like I want, so we will do this one using NDSolve. Let's solve for the different initial values for the curves we want to plot (say from to , every 2 units):

Now, let's combine the slope field with the solution curves:

This is, of course, hideous.  To fix that, we can explicitly tell it what region to plot: