This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 303 Review Sheet 1 Chapters 12 1. For each of the following first order ODE’s, use the given direction field to determine the behavior of y as t → ∞ . If the behavior depends on the initial value of y at t = 0, describe that dependency. (a) y = 1 + y . 1 3 t y 2 2 ! 2 ! 2 3 ! 1 1 ! 3 ! 1 ! 3 (b) y = 3 2 y . 1 3 t y 2 2 ! 2 ! 2 3 ! 1 1 ! 3 ! 1 ! 3 2. A. Solve following initial value problems for the given initial conditions. dy/dx = y 2 cosx, y (0) = 1 . B. Radium226 has a halflife of 1620 years. Find the time period during which a given amount of this material is reduced by twothirds. 3. Determine the order of the given differential equations, and also state whether the equation is linear or nonlinear. (a) ( t 2 + 1) d 3 y dt 3 2 = y. (b) y dy dt + y 2 d 2 y dt 2 = 1 + t 2 . (c) u xx + u yy = 0 . (d) u t + ( u xx ) 2 = 0 . 4. The halflife of a substance in the process of transformation is the amount of time it takes for onehalf of the substance to change. The standard model for this process isonehalf of the substance to change....
View
Full
Document
This note was uploaded on 11/29/2011 for the course MATH 303 taught by Professor Anderson,m during the Winter '08 term at BYU.
 Winter '08
 Anderson,M
 Math, Equations

Click to edit the document details