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**Unformatted text preview: **Jing Wang Assignment 1 MATH315, Winter 2012 due 01/21/2012 at 11:55pm EST. 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. 2 x 2 y 00 + 3 xy = y 2. y 00 + y = 3. y 00 + 13 y + 40 y = 4. y 00- 13 y + 40 y = A. y = e 5 x B. y = 1 x C. y = e- 8 x D. y = cos ( x ) 2. (1 pt) Match each of the differential equation with its solution. 1. y 00 + 8 y + 12 y = 2. y 00 + y = 3. xy- y = x 2 4. 2 x 2 y 00 + 3 xy = y A. y = x 1 2 B. y = e- 2 x C. y = 3 x + x 2 D. y = sin ( x ) 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 = 5exp ( 4 x ) , DIFFERENTIAL EQUATIONS 1. 2 x 2 y 00 + 3 xy = y 2. xy- y = x 2 3. y = 4 y 4. y 00 + y = 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 + 25 y = 2. dy dx =- 2 xy x 2- 5 y 2 3. d 2 y dx 2 + 8 dy dx + 16 y = 4. dy dx = 10 xy 5. dy dx + 12 x 2 y = 12 x 2 A. y = A cos ( 5 x )+ B sin ( 5 x ) B. 3 yx 2- 5 y 3 = C C. y = Ae 5 x 2 D. y = Ce- 4 x 3 + 1 E. y = Ae- 4 x + Bxe- 4 x 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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