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M251ex1(fa04) - NAME MATH 251 Fall 2004 Exam 1 Oct 12th...

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MATH 251 Fall 2004 Exam 1 Oct 12th, 2004 NAME : ID : INSTRUCTOR : There are 12 questions on 10 pages. Please read each problem carefully before starting to solve it. For each multiple choice problem 4 answers are given, only one of which is correct. Mark only one choice. For partial credit questions, all work must be shown - credit will not be given for an answer unsupported by work. N O CALCULATORS ARE ALLOWED . P LEASE DO NOT WRITE IN THE BOX BELOW . 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: Total:
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MATH 251 Fall 2004 Exam 1 1. (4 points) Identify each of the following equations as linear or non-linear and also determine their order. (a) y dy dt = t (b) parenleftBig d 2 y dt 2 parenrightBig 3 + ( dy dt ) 3 + y 3 = t 3 (c) sin ( t ) dy dt + t 5 y = (1 - t 2 ) d 2 y dt 2 (d) (1 + y ) sin 2 t + ( d 3 y dt 3 + y ) cos 2 t = 1 2. (6 points) The initial value problem (4 - t 2 ) y + ln ( t ) y = sin ( t ) y (1 . 33) = 3 . 14159 is certain to have a unique continuous solution on the interval (a) ( - 4 , 4) (b) ( - 2 , 2) (c) (0 , 2) (d) (0 , 3 . 14159) Page 2 of 10
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MATH 251 Fall 2004 Exam 1
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