# Exam1A - BUT DO NOT SOLVE the initial value problem whose...

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M427K EXAM 1A FALL, 2009 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. (12 points) Sketch an accurate graph of the solution of the initial value problem y 0 = ( y - 3)( y + 2) 2 , y (0) = 1 . Your y -axis must have a scale.

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YOUR SCORE: /100 2. (12 points) Find the general solution of the following diﬀerential equation, in explicit form if possible. y 0 = y 6 - 6 t 2 y 6 3. (12 points) Show that the following diﬀerential equation is NOT exact, but then solve the equation that results from multiplying the following equation by x . (3 x 2 y 2 + 6 e y ) dx + (2 x 2 y + 3 xe y + 1 x ) dy = 0
4. (12 points) Find the general solution of t 2 y 0 + 3 ty = sin t t on the interval t > 0. 5. (8 points) A 1000 liter tank initially contains 400 liters of water in which 1200 grams of dye are dissolved. A solution containing 2 grams per liter of dye runs in at 20 liters per minute, and the well-stirred solution runs out at 25 liters per minute. Write down

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Unformatted text preview: BUT DO NOT SOLVE the initial value problem whose solution gives the amount of dye in the tank t minutes after the process starts. 6. (12 points) Solve the following initial value problem. y 00 + 10 y + 25 y = 0 , y (0) = 4 , y (0) = 5 7. (12 points) Find the general solution of the following dierential equations. 4 y 00 + 4 y + 37 y = 0 8. (12 points) Suppose y ( t ) satises y = 3 t 2 + y 2 and y (1) = 0. Use Eulers Method with step size h = t = 0 . 1 to approximate y (1 . 2). DO NOT ROUND OFF! 9. (8 points) Determine the longest interval in which the dierential equation ( x + 5)( x-4) y 00 + 3 xy + (ln( | x | )) y = 0 has a unique twice dierentiable solution satisfying the given initial condition. (a) y (1) = y (1) = 3 (b) y (6) = y (6) = 18...
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## This note was uploaded on 01/27/2012 for the course MATH 427 k taught by Professor Goddard during the Fall '10 term at University of Texas at Austin.

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Exam1A - BUT DO NOT SOLVE the initial value problem whose...

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