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Unformatted text preview: . a) Show that the equation is not exact. Answer: Using , you can see . b) Multiply the equation by and show that the new equation is exact. Answer: Using the new , you can see . c) Solve the equation for the solution that satisfies . Answer: You have , so , so and the final solution is given implicitly by 6. (10 pts.) Consider the differential equation . Determine the region in the plane where a unique solution should exist. Answer: Using , and , you need to determine where and/or do not exist. This happens if , so the region is determined by 7. (15 pts.) Consider the differential equation , with . a) Write down the general formula used to calculate with the Improved Euler Method. Answer: . b) Use the Improved Euler formula to compute an approximate solution to the equation at , using a step size (you will need to take two steps). Answer: If you use then the formula becomes . Starting with , , , and using , and using , . Therefore...
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This test prep was uploaded on 04/06/2008 for the course MATH 302 taught by Professor Goldberg during the Spring '08 term at Johns Hopkins.
 Spring '08
 GOLDBERG
 Math, Differential Equations, Equations

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