Math303 Review 1

Math303 Review 1 - Math 303 Review Sheet 1 Chapters 1-2 1...

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Unformatted text preview: Math 303 Review Sheet 1 Chapters 1-2 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. Radium-226 has a half-life of 1620 years. Find the time period during which a given amount of this material is reduced by two-thirds. 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 half-life of a substance in the process of transformation is the amount of time it takes for one-half of the substance to change. The standard model for this process isone-half of the substance to change....
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Math303 Review 1 - Math 303 Review Sheet 1 Chapters 1-2 1...

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