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Consider the initial value problem y" + 2y + 5xy = 0, y(0)=-6, y(0)= -7. The first 5 Taylor polynomial approximations of the solution are plotted below. You will compute the terms in these approximations. 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),..., 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) (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. Remember to use + for all multiplications. Note that an entire row will be marked incorrect if anything in the row is incorrect. { (3) y (0) = -6 -6 y (0)- y" (0) (0)- (0)- ✓ term in Taylor series -6 term in Taylor series term in Taylor series term in Taylor series term in Taylor series

Consider the initial value problem y" + 2y + 5xy = 0, y(0)=-6, y(0)= -7. The first 5 Taylor polynomial approximations of the solution are plotted below. You will compute the terms in these approximations. 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),..., 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) (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. Remember to use + for all multiplications. Note that an entire row will be marked incorrect if anything in the row is incorrect. { (3) y (0) = -6 -6 y (0)- y" (0) (0)- (0)- ✓ term in Taylor series -6 term in Taylor series term in Taylor series term in Taylor series term in Taylor series

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the initial value problem y" + 2y + 5xy = 0, y (0)=-6, (0) = -7. The first 5 Taylor polynomial approximations of the solution are plotted below. You will compute the terms in these approximations. 0.0 1 2 ts 3 terms (3) Sto 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), 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), 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. Remember to use for all multiplications. Note that an entire row will be marked incorrect if anything in the row is incorrect. y (0) = -6 -6 y' (0)- y" (0)- 3) (0)- (0)- ✓ term in Taylor series -6 -6 term in Taylor series term Taylor series term in Taylor series term in Taylor series
Transcribed Image Text:Consider the initial value problem y" + 2y + 5xy = 0, y (0)=-6, (0) = -7. The first 5 Taylor polynomial approximations of the solution are plotted below. You will compute the terms in these approximations. 0.0 1 2 ts 3 terms (3) Sto 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), 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), 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. Remember to use for all multiplications. Note that an entire row will be marked incorrect if anything in the row is incorrect. y (0) = -6 -6 y' (0)- y" (0)- 3) (0)- (0)- ✓ term in Taylor series -6 -6 term in Taylor series term Taylor series term in Taylor series term in Taylor series
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