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
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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 dierential 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 dierential equation has the form you found in part (a). (c) (6 points) Determine so that the solution y ( t ) satisfying the dierential equation and the initial conditions y (0) = 1, y (0) = approaches 0 as t ....
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Exam1B - containing 2 grams per liter of dye runs in at 9...

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