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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## This note was uploaded on 01/21/2012 for the course MA 23200 taught by Professor Josephchen during the Spring '11 term at Purdue.

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

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