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Unformatted text preview: xx 2 sin y + e y ) dy + (3 y 3 e x + 2 x cos ycos x ) dx = 0 5. (12 points) Find the general solution of ( t 2 + 1) y + 4 ty = sin t t 2 + 1 + t. 6. (14 points) A 1000 liter tank is full of water in which 2000 grams of dye is dissolved. A solution containing 1 gram of dye per liter runs in at 20 liters per minute, and the wellstirred solution runs out at 30 liters per minute. How much dye is in the tank after 90 minutes? 7. (12 points) Suppose y ( t ) satisﬁes y = 3 t 2 + 2 y 2 and y (1) = 2. Use Euler’s Method with step size h = Δ t = 0 . 1 to approximate y (1 . 2). DO NOT ROUND OFF! 8. (12 points) For the initial value problem y = 3 t 2 + y 3 , y (0) = 0, let φ ( t ) = 0 and use the method of successive approximations to calculate φ 1 ( t ) and φ 2 ( t )....
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 Spring '08
 Fonken
 Kilogram, Boundary value problem, following differential equation

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