y" + 2y/ + 3zy = 0, y(0) = 4, / (0) = -9. The first 5 Taylor polynomial approximations of the solution are plotted below. You will compute the terms in these approximations. 1 term 2 terms 3 terms 12 4 terms 5 terms 10 0.0 Rewrite the differential equation in the form y/" = something, and enter that something in the top slot of the left column. Use y' for y'. Then by repeatedly differentiating that expression, obtain formulas for the derivatives y/3), ... , yl4), in terms of y and y/ and enter these in the left column below. Use these formulas to evaluate y (0), / (0), y" (0), ... , y/9 (0) for the solution of the IVP given above, and enter these numbers in the middle column. In the rightmost column, enter the corresponding terms of the Taylor series of the solution of the IVP. %3D
y" + 2y/ + 3zy = 0, y(0) = 4, / (0) = -9. The first 5 Taylor polynomial approximations of the solution are plotted below. You will compute the terms in these approximations. 1 term 2 terms 3 terms 12 4 terms 5 terms 10 0.0 Rewrite the differential equation in the form y/" = something, and enter that something in the top slot of the left column. Use y' for y'. Then by repeatedly differentiating that expression, obtain formulas for the derivatives y/3), ... , yl4), in terms of y and y/ and enter these in the left column below. Use these formulas to evaluate y (0), / (0), y" (0), ... , y/9 (0) for the solution of the IVP given above, and enter these numbers in the middle column. In the rightmost column, enter the corresponding terms of the Taylor series of the solution of the IVP. %3D
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:y" + 2y + 3zy = 0, y (0) = 4, y (0) = -9.
The first 5 Taylor polynomial approximations of the solution are plotted below. You will compute the terms in these approximations.
14
1 term
2 terms
12
3 terms
4 terms
5 terms
10
-0.2
0.0
0.2
0.4
Rewrite the differential equation in the form y" = something, and enter that something in the top slot of the left column. Use y' for y'.
Then by repeatedly differentiating that expression, obtain formulas for the derivatives y), ... , y(4), in terms of y and y' and enter these in the left
column below. Use these formulas to evaluate y (0), y (0), y" (0), ... , y/4) (0) for the solution of the IVP given above, and enter these numbers in the
middle column. In the rightmost column, enter the corresponding terms of the Taylor series of the solution of the IVP.
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