# Exam1B - containing 2 grams per liter of dye runs in at 9...

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M427K EXAM 1B SPRING, 2008 Dr. Schurle Your name: Your UTEID: Show all your work on these pages. Be organized and neat. Your work should be your own; there should be no talking, reading notes, checking laptops, using cellphones, . . . . 1. (10 points) Write down a diﬀerential equation of the form y 0 = ay + b such that y = - 5 / 6 is a solution and all other solutions converge to - 5 / 6 as t → ∞ .

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YOUR SCORE: /70 2. (10 points) Find the solution of the given initial value problem in explicit form. y 0 = (1 + 4 t 3 ) y 2 , y (2) = - 1 3. (10 points) Either solve the following diﬀerential equation or explain why none of the techniques covered so far will work. (2 ye x + 6 y ) dy dx + y 2 e x - 4 cos x = 0
4. (10 points) Find the general solution of (70 + t ) y 0 + 2 y = 18(70 + t ). 5. (10 points) A 300 liter tank initially contains 210 liters of pure water. A solution

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Unformatted text preview: containing 2 grams per liter of dye runs in at 9 liters per minute, but due to needs ”downstream” from the tank, the well-stirred solution must run out at 6 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 y-21 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.

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Exam1B - containing 2 grams per liter of dye runs in at 9...

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