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The general solution of the equation = (1+²) cosx 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)=1.5 the solution y(x) = tan (tan (1.5)+ sinx) has a vertical asymptote at x = -tan (1.5) 0.62859. Use Euler's method to verify this fact empirically. C Complete the following table using the indicated values of h to approximate y(x) for three points leading up to the asymptote. h=0.1 h=0.01 X y 0.4 0.5 0.6 (Do not round until the final answer. Then round to four decimal places as needed.). 300

The general solution of the equation = (1+²) cosx 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)=1.5 the solution y(x) = tan (tan (1.5)+ sinx) has a vertical asymptote at x = -tan (1.5) 0.62859. Use Euler's method to verify this fact empirically. C Complete the following table using the indicated values of h to approximate y(x) for three points leading up to the asymptote. h=0.1 h=0.01 X y 0.4 0.5 0.6 (Do not round until the final answer. Then round to four decimal places as needed.). 300

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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The general solution of the equation dx = (1 + y²) 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 with y(0) = 1.5 the -tan (1.5) 0.62859. Use Euler's method to verify this fact empirically. solution y(x) = tan (tan (1.5)+ sinx) has a vertical asymptote at x = CEITE Complete the following table using the indicated values of h to approximate y(x) for three points leading up to the asymptote. h=0.1 h=0.01 y y 0.4 11 0.5 0.6 (Do not round until the final answer. Then round to four decimal places as needed.) 4
Transcribed Image Text:The general solution of the equation dx = (1 + y²) 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 with y(0) = 1.5 the -tan (1.5) 0.62859. Use Euler's method to verify this fact empirically. solution y(x) = tan (tan (1.5)+ sinx) has a vertical asymptote at x = CEITE Complete the following table using the indicated values of h to approximate y(x) for three points leading up to the asymptote. h=0.1 h=0.01 y y 0.4 11 0.5 0.6 (Do not round until the final answer. Then round to four decimal places as needed.) 4
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