{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hw2 - Consider the ﬁrst-order equation dx dt = x 2-1(1(a...

This preview shows page 1. Sign up to view the full content.

Math 454 Problem Set #2 Fall 2008 Sect. 1 Due Thursday, 9/11, at the beginning of class. Reminder. You are encouraged to work together on homework problems. How- ever, the ﬁnal write-up must be your own. You will be quizzed on some of these problems, so be sure you can do all the problems without help. Also, unless otherwise stated, all reading assignments are from the text. Read: Sects. 2.5-7; 3.0, 3.1 Problems (note that the problems for Ch. 2 begin on p. 36 of the text): - Sect. 2.5 #1, 4, 5(b), 6 - Sect. 2.6 #1 - Sect. 2.7 #1, 4 - Sect. 3.1 #1, 3 P1. (Finding the blow-up time)
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Consider the ﬁrst-order equation dx dt = x 2-1 . (1) (a) Show that Z x 1 x dx x 2-1 = Z t 1 t dt (2) holds for all trajectories x ( t ) with x ( t ) = x and x ( t 1 ) = x 1 . (b) Suppose a trajectory starts at x = 2 at t = 0 . At what time does it reach x = ∞ ? (c) For a general initial value problem ˙ x = f ( x ) , x (0) = x , suppose f ( x ) > for all x ≥ x . Can you formulate a condition for x ( t ) → ∞ in ﬁnite time? Hint: You can state your answer in terms of an integral similar to that in Eq. (2)....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online