dev12384 - x 2 + xy ) dy = 0. Question 2. 1. Use the xed...

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MAT 2384A-Fall 2009-Homework #1 To be submitted in class on Friday, September 25 Question 1. For each of the following ODEs, Find the General Solution. If an initial condition is given, ﬁnd the corresponding particular solution. 1. y p 1 + y 2 y 0 = xe x , y (1) = 3 2. 4 xyy 0 + 3 x 2 + 2 y 2 = 0 , y (1) = 1 3. ( y 2 e xy 2 + 4 x 3 ) dx + (2 xye xy 2 - 3 y 2 ) dy = 0 4. (cos y + y cos x ) dx + (sin x - x sin y ) dy = 0 , y ( π/ 2) = π/ 4 5. (1 + y 2 ) y 0 = y cos x, y (0) = 1 6. ( 1 x - e y ) dx + (sin y - xe y ) dy = 0 , y (1) = 0 7. (2 xy 4 e y + 2 xy 3 + y ) dx + ( x 2 y 4 e y - x 2 y 2 - 3 x ) dy = 0 8. (3 xy + y 2 ) dx + (
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Unformatted text preview: x 2 + xy ) dy = 0. Question 2. 1. Use the xed point iteration method to nd the root of x 4 + 6 x-5 in the interval [0 , 1] to 5 decimal places. 2. Use Newtons Method to nd 3 7 to 6 decimal places. Start with x = 2 . 3. . Use Newtons Method to nd the positive solution of e x = 2cos x to 6 decimal places. Start with x = 1. 1...
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This note was uploaded on 02/24/2010 for the course SITE MAT2384 taught by Professor Josephkhoury during the Fall '09 term at University of Ottawa.

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