M251ex1(sp03) - MATH 251 Midterm Exam I Spring 2003 NAME...

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Unformatted text preview: MATH 251 Midterm Exam I Spring 2003 NAME STUDENT NUMBER INSTRUCTOR There are 11 questions on 9 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. ( 6 pt) 3. ( 6 pt) 4. ( 6 pt) 5. ( 6 pt) 6. (10 pt) 7. (14 pt) 8. (10 pt) 9. (12 pt) 10.(12 pt) 11.(10 pt) Total MATH 251 Midterm Exam I PAGE 2 1. (8 points) Classify the following differential equations as linear or non-linear and state their order. linear/ order non-linear ln( t ) d 2 y dt 2 + 3 e t dy dt- y sin t = 0 2 y- y 2 = e t y 000 + ( t 2- 1) y + cos t = 0 y 00- sin( t + y ) y + ( t 2 + 1) y = 0 2. (6 points) What is the integrating factor of the differential equation t 2 y 00- 4 ty = e t- cos 2 t (a) μ ( t ) = 1 /t 4 (b) μ ( t ) = e 4 ln t (c) μ ( t ) =- t 4 (d) μ ( t ) =- 2 t 2 Page 2 MATH 251 Midterm Exam I PAGE 3 3. (6 points) The Existence and Uniqueness Theorem guarantees that the solution to3....
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This note was uploaded on 07/23/2008 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Pennsylvania State University, University Park.

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M251ex1(sp03) - MATH 251 Midterm Exam I Spring 2003 NAME...

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