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1 The general solution of the equation = (1+ y²) cos x is y(x) = tan (C + sin x). With the initial condition y(0) = 0, the solution y(x) = tan (sin x) is well behaved. But with y(0) = 2.6 the solution y(x) = tan (tan ¯ 1 (2.6) + sin x) has a vertical asymptote at x=x-tan − 1 (2.6) = 0.37597. Use Euler's method to verify this fact empirically. Complete the following table using the indicated values of h to approximate y(x) for three points leading up to the asymptote. h=0.05 y 0.25 h=0.005 0.3 0.35 (Do not round until the final answer. Then round to four decimal places as needed.)

1 The general solution of the equation = (1+ y²) cos x is y(x) = tan (C + sin x). With the initial condition y(0) = 0, the solution y(x) = tan (sin x) is well behaved. But with y(0) = 2.6 the solution y(x) = tan (tan ¯ 1 (2.6) + sin x) has a vertical asymptote at x=x-tan − 1 (2.6) = 0.37597. Use Euler's method to verify this fact empirically. Complete the following table using the indicated values of h to approximate y(x) for three points leading up to the asymptote. h=0.05 y 0.25 h=0.005 0.3 0.35 (Do not round until the final answer. Then round to four decimal places as needed.)

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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1 The general solution of the equation = = (1 + y²) cos x is y(x) = tan (C + sin x). With the initial condition y(0) = 0, the solution y(x) = tan (sin x) is well behaved. But with y(0) = 2.6 the solution y(x) = tan (tan ¯ 1 (2.6) + sin x) has a vertical asymptote at x= - tan¯ - (2.6) 0.37597. Use Euler's method to verify this fact empirically. Complete the following table using the indicated values of h to approximate y(x) for three points leading up to the asymptote. h = 0.05 h = 0.005 0.25 0.3 177 0.35 (Do not round until the final answer. Then round to four decimal places as needed.)
Transcribed Image Text:1 The general solution of the equation = = (1 + y²) cos x is y(x) = tan (C + sin x). With the initial condition y(0) = 0, the solution y(x) = tan (sin x) is well behaved. But with y(0) = 2.6 the solution y(x) = tan (tan ¯ 1 (2.6) + sin x) has a vertical asymptote at x= - tan¯ - (2.6) 0.37597. Use Euler's method to verify this fact empirically. Complete the following table using the indicated values of h to approximate y(x) for three points leading up to the asymptote. h = 0.05 h = 0.005 0.25 0.3 177 0.35 (Do not round until the final answer. Then round to four decimal places as needed.)
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