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math1005ass1

# math1005ass1 - method of undetermined coeﬃcients 1(7...

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Total of 40 marks MATH1005A, Summer2009 Assignment 1 Problem 1 . Show that if ( Q x - P y ) /P is a function of y alone, then the equation I y P + IP y = I x Q + IQ x enables us to find an integrating factor for P + Qy 0 = 0 ( 4 marks ). Use this method to solve the equation y - 6 x 2 y 3 + (2 x - 8 x 3 y 2 ) y 0 = 0 . (8 marks) Problem 2 . Solve the differential equations or initial value problems using the
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Unformatted text preview: method of undetermined coeﬃcients. 1. (7 marks) y 00 + 2 y + 2 y = x 3-1. 2. (7 marks) y 00-7 y + 12 y = sin x-cos x . 3. (7 marks) y 00 + 2 y + y = e 2 x . 4. (7 marks) y 00 + 2 y = e x sin x, y (0) = 1 , y (0) = 1....
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