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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 nonlinear and state their order. linear/ order nonlinear 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.
 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations

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