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Unformatted text preview: containing 2 grams per liter of dye runs in at 12 liters per minute, but due to needs ”downstream” from the tank, the wellstirred solution must run out at 8 liters per minute. How much dye is in the tank at the instant the tank becomes full? Hint: see some of your earlier work. 6. Consider the diﬀerential equation y 00 + 4 y21 y = 0 . (a) (8 points) Find its general solution. (b) (6 points) Explain how you know that every solution of the diﬀerential equation has the form you found in part (a). (c) (6 points) Determine α so that the solution y ( t ) satisfying the diﬀerential equation and the initial conditions y (0) = 1, y (0) = α approaches 0 as t → ∞ ....
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This note was uploaded on 09/27/2008 for the course M 427K taught by Professor Fonken during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Fonken
 Calculus

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