Assignment #1 solutions

Assignment #1 Solutions
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Stephanie Campbell Assignment 1 MATH263, Fall 2010 due 09/12/2010 at 11:55pm EDT. You may attempt any problem an unlimited number of times. 1. (1 pt) Match each of the following differential equations with a solution from the list below. 1. y 00 + y = 0 2. 2 x 2 y 00 + 3 xy 0 = y 3. y 00 - 12 y 0 + 32 y = 0 4. y 00 + 12 y 0 + 32 y = 0 A. y = e - 8 x B. y = 1 x C. y = e 4 x D. y = cos ( x ) Correct Answers: D B C A 2. (1 pt) Match each of the differential equation with its solution. 1. y 00 + 13 y 0 + 40 y = 0 2. 2 x 2 y 00 + 3 xy 0 = y 3. xy 0 - y = x 2 4. y 00 + y = 0 A. y = 3 x + x 2 B. y = e - 8 x C. y = x 1 2 D. y = sin ( x ) Correct Answers: B C A D 3. (1 pt) Match each differential equation to a function which is a solution. FUNCTIONS A. y = 3 x + x 2 , B. y = e - 8 x , C. y = sin ( x ) , D. y = x 1 2 , E. y = 4exp ( 6 x ) , DIFFERENTIAL EQUATIONS 1. y 00 + 12 y 0 + 32 y = 0 2. y 0 = 6 y 3. 2 x 2 y 00 + 3 xy 0 = y 4. xy 0 - y = x 2 Correct Answers: B E D A 4. (1 pt) Match the following differential equations with their solutions. The symbols A , B , C in the solutions stand for arbitrary con- stants. You must get all of the answers correct to receive credit. 1. d 2 y dx 2 + 81 y = 0 2. dy dx = - 2 xy x 2 - 9 y 2 3. d 2 y dx 2 + 12 dy dx + 36 y = 0 4. dy dx = 18 xy 5. dy dx + 18 x 2 y = 18 x 2 A. y = Ce - 6 x 3 + 1 B. 3 yx 2 - 9 y 3 = C C. y = A cos ( 9 x )+ B sin ( 9 x ) D. y = Ae 9 x 2 E. y = Ae - 6 x + Bxe - 6 x Correct Answers: C B E D A 5. (1 pt) Just as there are simultaneous algebraic equations (where a pair of numbers have to satisfy a pair of equations)
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