M345t1CS11Sol - Embry-Riddle Aeronautical University C...

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Unformatted text preview: Embry-Riddle Aeronautical University C. Jacobs MA 345 Differential Equations Spring 2011 Exam I Questions 1 - 4 (16 points). Match each of the following differential equations with the method of solution. 1. ( x 2 + y 2 ) dx- x 2 dy = 0 a ) Separation of variables 2. ( x 2 y 2- y 2 ) dx- dy = 0 b ) Exact 3. ( x 2 + y 2 ) dx + 2 xy dy = 0 c ) First order linear 4. 1- x y dx + x 2 y dy = 0 d ) Substitution v = y x Solutions: (1) matches (d) (2) matches (a) (3) matches (b) (4) matches (c) 5. (6 points) Suppose a tank contains 1 gram of salt dissolved in 12 liters of water. At t = 0, a hole is drilled in the bottom of the tank and fluid leaks out at 3 liters per minute. At the same time, fresh water is pumped into the tank at 1 liter per minute. Let x ( t ) be the amount (in grams) of salt in the tank after t minutes. Which differential equation correctly determines x ( t ) ? dx dt = Rate In- Rate out = 0- x ( t ) grams 12- 2 t liters · 3 liters minute =- 3 x ( t ) 12- 2 t a ) dx dt = 1- 3...
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This note was uploaded on 03/20/2011 for the course MA 243 taught by Professor Poon during the Spring '09 term at Embry-Riddle FL/AZ.

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M345t1CS11Sol - Embry-Riddle Aeronautical University C...

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