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Unformatted text preview: 10 = 0 . 12 solve for t 2 = 13. 5a) The Chain Rule gives w x = af , w xx = a 2 f etc. So you only need f to be twice dierentiable and a 2 + b 2 = 1. It means that many wave shapes are possible. 5b) A particular solution is y p = 2 = c 3 . Then we know that the general solution is of the form y = c 1 cos(2 t ) + c 2 sin(2 t ) + 2. To get the initial conditions you choose y = 1 . 5 cos(2 t ) + 2 . 05 sin(2 t ) + 2 6) Eulers method replaces dy dx = x 2 + y 2 by y n +1y n h = x 2 n + y 2 n . With h = . 1 you have x = 0, x 1 = . 1, x 2 = . 2, and y =1. Then y 1y h = x 2 + y 2 , y 1 + 1 . 1 = 1 , so y 1 =. 9. Then y 2y 1 h = x 2 1 + y 2 1 , y 2 + . 9 . 1 = . 01 + . 81 so y 2 =. 9 + . 082 =. 818. 7...
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This note was uploaded on 01/21/2011 for the course MATH 2930 taught by Professor Terrell,r during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 TERRELL,R

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