dev42384 - y = 0 y(0 =-1 y(0 = 0 y 00(0 =-1 7 y 000 y 00 2...

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MAT 2384A-Fall 2009-Homework #4 To be submitted before class on Tuesday, October 20 Question 1. Solve each of the following ODE. If initial conditions are give, give the unique Solution. 1. x 2 y 00 + xy 0 + 4 y = 0 , x > 0 2. x 2 y 00 - 6 y = 0 , x > 0 , y (1) = 5 , y 0 (1) = 5 3. x 2 y 00 + 5 xy 0 + 4 y = 0 , x > 0 , y (1) = 5 , y 0 (1) = - 9 4. y 000 - 5 y 00 + 2 y 0 + 8 y = 0 , y (0) = 2 , y 0 (0) = - 1 , y 00 (0) = - 5 5. y 000 + 9 y 00 + 27 y 0 + 27 y = 0 , y (0) = 2 , y 0 (0) = 0 , y 00 (0) = 3 6. y 000 + 5 y 00 + 8 y 0 + 4
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Unformatted text preview: y = 0 , y (0) =-1 , y (0) = 0 , y 00 (0) =-1 7. y 000 + y 00 + 2 y + 2 y = 0 . Question 2. Given that f (0) = 0, f (1) =-1 . 2546, f (2) = 1 . 1478 and f (3) = 2 . 2541 for some unknown function f , use Newton-Gregory’s forward difference formula to estimate the value of f at x = 2 . 5. 1...
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