M251ex1(fa02)

# M251ex1(fa02) - MATH 251 Midterm Exam I Fall 2002 NAME...

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MATH 251 Midterm Exam I Fall 2002 NAME STUDENT NUMBER INSTRUCTOR There are ?? questions on ?? pages. Please read each problem carefully before starting to solve it. Show all work – credit will not be given for an answer unsupported by work . N O CALCULATORS ARE ALLOWED . Point - grader use only 1. ( 8 pt) 2. (10 pt) 3. (12 pt) 4. (12 pt) 5. (10 pt) 6. (12 pt) 7. (12 pt) 8. (12 pt) 9. (12 pt) Total

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MATH 251 Midterm Exam I PAGE 2 1. (8 points) (a) Classify the following differential equations as linear or non-linear and state their order. linear/ order non-linear t 2 d 2 y dt 2 + 3 t dy dt - y sin t = 0 2 y 0 - sin y = 0 y 000 - 3 y 0 + y + t = 0 (b) Which of the linear differential equations above are homogeneous? Page 2
MATH 251 Midterm Exam I PAGE 3 2. (10 points) Find the general solution. (a) y 00 - 4 y 0 + 13 y = 0 (b) y 00 + 2 y 0 + y = 0 Page 3

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Midterm Exam I PAGE 4 3. (12 points) Find the explicit solution of the initial value problems (a) y 0 = cos t +1 y , y (0) = - 3 . (b)
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M251ex1(fa02) - MATH 251 Midterm Exam I Fall 2002 NAME...

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