232sampleexam3solution

232sampleexam3solution - MA 23200 NAME: PUID: Exam 3...

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MA 23200 NAME: Exam 3 PUID: INSTRUCTIONS No books or notes are allowed. You may use a one-line scientific calculator. No other electronic device is allowed. Be sure to turn off your cellphone. Show all your work in the space provided. Little or no credit may be given for an answer with insufficient or inconsistent work, even if the answer happens to be correct. Write answers in the boxes provided. All answers are expected to be simplified ( 2 4 1 2 , 2 x + x 3 x , e ln 2 2, etc). Question Possible Score 1 5 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 15 To approximate the solution to y 0 = f ( x,y ), y ( x 0 ) = y 0 using Euler’s method with increments of Δ x , we use the formula y n +1 = y n + f ( x n ,y n x where y n = y ( x n ). 1
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1.) (5 pts) Consider the initial value problem y 0 + 1 x 2 - 1 y = sin x 2 x - 9 y (2) = 0 . What is the largest interval on which a unique continuous solution will exist? Do not attempt to find the solution. Solution: p ( x ) = 1 x 2 - 1 q ( x ) = sin x 2 x - 9 Points of discontinuity occur at x = - 1, 1 and 9 2 = 4 . 5. The initial condition,
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232sampleexam3solution - MA 23200 NAME: PUID: Exam 3...

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