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cos x is y(x)=tan (C+ sinx). With the initial condition y(0)=0, the solution y(x)=tan (sin x) is well behaved. But The general solution of the equation=(1+y²) with y(0) = 2.6 the solution y(x) = tan (tan (2.6) + sin x) has a vertical asymptote at x = =-tan¹(2.6) 0.37597. Use Euler's method to verify this fact 1 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 x y 0.25 0.3 O

cos x is y(x)=tan (C+ sinx). With the initial condition y(0)=0, the solution y(x)=tan (sin x) is well behaved. But The general solution of the equation=(1+y²) with y(0) = 2.6 the solution y(x) = tan (tan (2.6) + sin x) has a vertical asymptote at x = =-tan¹(2.6) 0.37597. Use Euler's method to verify this fact 1 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 x y 0.25 0.3 O

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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dy The general solution of the equation = (1+²) cos x is y(x) = tan (C+ sinx). With the initial condition y(0)=0, the solution y(x)= tan (sin x) is well behaved. But dx 1 with y(0) = 2.6 the solution y(x) = tan (tan ¹(2.6) + sin x) has a vertical asymptote at x = - tan¹(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 h=0.005 y x 0.25 0.3 0.35 (Do not round until the final answer. Then round to four decimal places as needed.)
Transcribed Image Text:dy The general solution of the equation = (1+²) cos x is y(x) = tan (C+ sinx). With the initial condition y(0)=0, the solution y(x)= tan (sin x) is well behaved. But dx 1 with y(0) = 2.6 the solution y(x) = tan (tan ¹(2.6) + sin x) has a vertical asymptote at x = - tan¹(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 h=0.005 y x 0.25 0.3 0.35 (Do not round until the final answer. Then round to four decimal places as needed.)
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