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Practice_exam1

# Practice_exam1 - 3 days Initially it covers 1 of the pond...

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MA 262 Practice Exam I Name: PUID: Section: SHOW ALL YOUR WORK. NO CALCULATORS, BOOKS, OR PAPERS ARE ALLOWED. Points awarded 1. (12 points) 2. (10 points) 3. (12 points) 4. (10 points) 5. (10 points) 6. (12 points) 7. (10 points) 8. (12 points) 9. (12 points) Total Points: 1

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1. (12 points) Solve the initial value problem dy dx = xy x - 1 , y (0) = 1 . 2. (10 points) Find the general solution of x dy dx - 4 y = x 5 . 3. (12 points) Solve the following initial value problem. You may leave your solution in implicit form. y 2 - xy xy 2 dx + ( x y 2 + 2 y ) dy = 0 , y (1) = 2 . 4. (10 points) Find the general solution of x 2 y = xy + x x 2 - y 2 . 2
5. (10 points) Find the general solution of y + y = e x y 2 . 6. (12 points) Slime is growing on the surface of a pond. It doubles the area it covers every
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Unformatted text preview: 3 days. Initially it covers 1% of the pond. How long will it take to cover the whole pond? 7. (10 points) For what values of a, b and c is it true that [ 1 0 0 2 ][ a b c ] = [ a b c ][ 1 0 0 2 ] 8. (12 points) Solve the general solution to ( x-1)( x-2) y ′′ = y ′-1 , x > 2 . 9. (12 points) A solution containing 3 g/liter of salt ﬂows in a 60 liter tank at a rate of 6 liters/min. Initially the tank is half full of pure water. The well stirred mixture ﬂows out at a rate of 4 liters/min. How much salt (in grams) is in the tank when it overﬂows? 3...
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Practice_exam1 - 3 days Initially it covers 1 of the pond...

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