Pre-Calc Homework Solutions 278

Pre-Calc Homework Solutions 278 - 278 16. (a) Section 6.6...

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16. (a) } d d y x } 5 y 2 1 E } y d 2 y 1 } 5 E dx ln ) y 2 1 ) 5 x 1 C ) y 2 1 ) 5 e x 1 C y 2 1 56 e C e x y 5 Ae x 1 1 Initial condition: y (0) 5 3 3 5 Ae 0 1 1 2 5 A Solution: y 5 2 e x 1 1 y (1) 5 2 e 1 1 < 6.4366 (b) To find the approximation, set y 1 5 y 2 1 and use EULERT with initial values x 5 0 and y 5 3 and step size 0.2 for 5 points. This gives y (1) < 5.9766; error < 0.4599. (c) Use step size 0.1 for 10 points. This gives y (1) < 6.1875; error < 0.2491. (d) Use step size 0.05 for 20 points. This gives y (1) < 6.3066; error < 0.1300. 17. The exact solution is y 52 } x 2 2 2 1 x 1 2 } , so y (3) 52 0.2. (a) To find the approximation, set y 1 5 2 y 2 ( x 2 1) and use IMPEULT with initial values x 5 2 and y 52} 1 2 } and step size 0.2 for 5 points. This gives y (3) < 2 0.2024; error < 0.0024. (b) Use step size 0.1 for 10 points. This gives y (3) < 2 0.2005; error < 0.0005. (c) Use step size 0.05 for 20 points. This gives y (3) 52 0.2001; error < 0.0001. (d)
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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