Homework #6, due Monday 10/26/98

p177: 	3,4,5

p178: 	9. Typo alert! The question should read "... on any open
		interval of t0 if x(t0)=1."

X (grad students only)
	Show that the Fundamental E/U theorem applies also to 
	the non-autonomous system x'=f(x,t) where f is C^1 on
	E x (-h,h) for some h>0. (x0 is in E and t0 is in (-h,h).
	Hint: nonautonomous systems can be converted to autonomous ones!

XX	

XXX	Bearing in mind what we discussed in class on Wed (10/21),
	make sketches of every qualitatively distinct solution that
	can exist for x'=f(x) with f:W -> R, W an open subset of R
	(i.e. the autonomous 1D equation). (It's up to you to decide
	an appropriate definition of "qualitative".)
	(b) What are your initial thoughts on doing the same for 2D
	systems? (c) 3D?