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Unformatted text preview: MthSc 208, Spring 2011 (Differential Equations) Dr. Macauley HW 4 Due Friday February 4th, 2011 (1) Use the integrating factor method to find the general solution of the following differential equations. (a) 2 y 3 y = 5 (b) y + 2 ty = 5 t (c) ty = 4 y + t 4 (2) Use the varation of parameters method to find the general solution of the following differ ential equation. Then find the particular solution satisfying the given initial condition. (a) y 3 y = 4 , y (0) = 2 (b) y + y = e t , y (0) = 1 (c) y + 2 ty = 2 t 3 , y (0) = 1. (3) A murder victim is discovered at midnight at the temperature of the body is recorded at 31 ◦ C, and it was discovered that the proportionality constant in Newton’s law was k = ln(5 / 4). Assume that at midnight the surrounding air temperature A ( t ) is 0 ◦ C, and is falling at a constant rate of 1 ◦ C per hour. At what time did the victim die? (Set T ( t ) = 37 and solve for t – use a computer or calculator for this part.) Hint : Letting t = 0 represent midnight will simplify your calculations.represent midnight will simplify your calculations....
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 Spring '09
 Staufeneger
 Differential Equations, Equations, TP, Ambient Temperature, particular solution Tp

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