HW4_2384f10 - x i , f i ) with f i = f ( x i ) for some...

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MAT 2384A-Fall 2010-Homework #4 To be submitted in class on Tuesday, November 9 Question 1. For each of the following nonhomogeneous ODEs, Find the General Solution. If an initial condition is given, find the corresponding unique solution. 1. y 00 - 2 y 0 + 2 y = x 2 , y (0) = 1 , y 0 (0) = - 1 2. y 000 + 4 y 0 = 3 x + cos(2 x ) , y (0) = 1 , y 0 (0) = 0 , y 00 (0) = - 1 3. x 3 y 000 - 3 x 2 y 00 + 4 xy 0 - 4 y = 1 x , x > 0 4. y 00 + y = 1 cos x 5. x 2 y 00 + 3 xy 0 - 3 y = 1 x 2 , x > 0 , y (1) = 2 , y 0 (1) = 0 6. y 000 + y 00 + 9 y 0 + 9 y = 2 e - x + 60 sin(3 x ). Question 2. Given the set of 4 data points; (1 , 0 . 8415) , (1 . 25 , 1 . 0610) , (1 . 5 , 1 . 2217) , (1 . 75 , 1 . 3017) where each point is of the form (
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Unformatted text preview: x i , f i ) with f i = f ( x i ) for some unknown function f . 1. Use the Newtons Forward Dierence Interpolation polynomial of degree 3 (with coecients rounded to 4 decimal places) to interpolate a value of f (1 . 6). 2. Given that 1 . 0446 | f (4) ( t ) | 2 . 0126 for any t [1 , 1 . 75], give bounds for the error in your estimation of f (1 . 6). 1...
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