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3. Given that dy +2 - ylnz 0 and that y = dr O when r=1, find the first three non – zero terms in the Taylor series expansion of y for values of z close to 1. (i) Find the value of y whenr 0.9. Hence, or otherwise, use the approximation dy 2h E Vn+1 - Y, 1 and a step length of 0.1 to find (ii) the value of y when z= 1.3, giving your final answer correct to 4 decimal places.

3. Given that dy +2 - ylnz 0 and that y = dr O when r=1, find the first three non – zero terms in the Taylor series expansion of y for values of z close to 1. (i) Find the value of y whenr 0.9. Hence, or otherwise, use the approximation dy 2h E Vn+1 - Y, 1 and a step length of 0.1 to find (ii) the value of y when z= 1.3, giving your final answer correct to 4 decimal places.

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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3. Given that 2- ylnz = 0 and that y 0 when r = 1, find the first three %3D non – zero terms in the Taylor series expansion of y for values of z close to 1. (1) Find the value of y whenr= 0.9. Hence, or otherwise, use the approximation dy 2h E Un+1 - Y, 1 and a step length of 0.1 to find dr) (ii) the value of y when z = 1.3, giving your final answer correct to 4 decimal places.
Transcribed Image Text:3. Given that 2- ylnz = 0 and that y 0 when r = 1, find the first three %3D non – zero terms in the Taylor series expansion of y for values of z close to 1. (1) Find the value of y whenr= 0.9. Hence, or otherwise, use the approximation dy 2h E Un+1 - Y, 1 and a step length of 0.1 to find dr) (ii) the value of y when z = 1.3, giving your final answer correct to 4 decimal places.
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