Exam1A - containing 2 grams per liter of dye runs in at 12 liters per minute but due to needs ”downstream” from the tank the well-stirred

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M427K EXAM 1A 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 = - 3 / 4 is a solution and all other solutions converge to - 3 / 4 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 + 3 t 2 ) 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. ( x 2 e y - 4 sin y ) dy dx + 2 xe y + 6 x = 0
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4. (10 points) Find the general solution of (60 + t ) y 0 + 2 y = 24(60 + t ). 5. (10 points) A 400 liter tank initially contains 240 liters of pure water. A solution
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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 well-stirred 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 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 at Austin.

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Exam1A - containing 2 grams per liter of dye runs in at 12 liters per minute but due to needs ”downstream” from the tank the well-stirred

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