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Unformatted text preview: y ( t ) = K/ (1 + Ae-kt ) is a solution to this equation for any A > 0.) We are given an initial condition so we can solve for A : y (0) = 15 = 60 1 + A 1 + A = 60 15 A = 4-1 = 3 Then y (1) = 60 1 + 3 e-. 05 . (b) What is the population of the penguins in the limit (as t goes to inﬁnity)? Taking the limit as t goes to inﬁnity, we have lim t →∞ 60 1 + 3 e-. 05 t = 60 3. (2 points) For each ﬁrst order diﬀerential equation below, state whether it is linear, separable, both, or neither. dy dx = yx + 5 y x 2 This one is both. Separable: dy/dx = y [( x +5) /x 2 ]. Linear: dy/dx-[( x +5) /x 2 ] y = 0. dy dx = y 2 + e x This one is neither....
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This note was uploaded on 03/25/2011 for the course MATH 1B taught by Professor Reshetiken during the Fall '08 term at Berkeley.
- Fall '08