Problems are from Blanchard, Devaney, and Hall, 2nd ed., unless otherwise noted.
[1.3] A qualitative technique: slope fields
8. First use Maple to make your own slope field for this problem, using
the same ranges as in the book. Use the Lab 2 assignment to help
you recall how to use "dfieldplot".
14. Sketch of slope fields from graph of RHS of DE.
15. Matching slope fields with DEs.
[1.5] Existence and uniqueness of solutions
2. Qualitative prediction from limited info.
14. Example of blow-up in finite time.
18. Example of non-uniqueness of solutions.
Also: (a.ii) Find a constant solution and a solution of the form
v = A t3, both of which satisfy the IC v(0)=0.
[1.6] Phase line for autonomous DEs
2. (Locate equilibria, sketch graph of RHS vs. y, classify the equilibria,
and sketch the phase line.)
14. (Sketch several solutions from phase line sketches of Problem 2.)
Use the following ICs: y(0)=9,7,0,-4 (not the ones in the book).
30,32,34,36. Sketch of phase line from graph of RHS, and vice versa.