WrittenHW04-Solutions

# WrittenHW04-Solutions - Math 216 (Section 50) Written...

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Unformatted text preview: Math 216 (Section 50) Written Homework #4 Solutions Fall 2007 1 ( 3.12 ) Verification y 1 = (cos 2 x ) =- 2 sin 2 x, y 00 1 =- 2(sin 2 x ) =- 4 cos 2 x =- 4 y 1 . Thus y 00 1 + 4 y 1 = 0 . X Also y 2 = (sin 2 x ) = 2 cos 2 x, y 00 2 = 2(cos 2 x ) =- 4 sin 2 x =- 4 sin 2 x =- 4 y 2 . Thus y 00 2 + 4 y 2 = 0 . X Particular Solution Set y ( x ) = c 1 y 1 + c 2 y 2 = c 1 cos 2 x + c 2 sin 2 x. Then y ( x ) =- 2 c 1 sin 2 x + 2 c 2 cos 2 x. Using the initial conditions y (0) = 3 and y (0) = 8, y (0) = c 1 = 3 , y (0) = 2 c 2 = 8 = c 2 = 4 . Solving these yields c 1 = 3 , c 2 = 4 . Thus the particular solution is written as follows: y ( x ) = 3 cos 2 x + 4 sin 2 x 2 ( 3.17 ) Verification y 1 = (1) = 0 , y 00 1 = 0 . Thus y 00 1 + y 1 = 0 . X Also y 2 = ( e- x ) =- e- x , y 00 2 =- ( e- x ) = e- x . Thus y 00 2 + y 2 = e- x- e- x = 0 . X 1 Particular Solution Set y ( x ) = c 1 y 1 + c 2 y 2 = c 1 + c 2 e- x ....
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## This homework help was uploaded on 04/02/2008 for the course ENGR 101 taught by Professor Ringenberg during the Fall '07 term at University of Michigan.

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WrittenHW04-Solutions - Math 216 (Section 50) Written...

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