Explanation Given information: The y ' = g ( t , y ) = t y where 1 ≤ t ≤ 2 with the initial condition y ( 1 ) = 4 Graph: Firstly, find the values of ( t 0 , y 0 ) , ( t 1 , y 1 ) , ( t 2 , y 2 ) using Euler’s method with number of iterations n = 2 . Here, g ( t , y ) = t y , a = 1 , b = 2 , t 0 = 1 y 0 = 4 , n = 2 So, h = b − a n = 2 − 1 2 = 0.5 Now, by using the formulas t 1 = t 0 + h = 1 + 0.5 = 1.5 and y 1 = y 0 + ( g ( t 0 , y 0 ) × h ) = 4 + ( g ( 1 , 4 ) × 0.5 ) = 4 + ( ( 1 × 4 ) × 0

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ISBN: 9780137590810

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar, William Edward Tavernetti

Publisher: PEARSON

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Chapter 10.7, Problem 2CYU

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To graph: The polygonal path corresponding to the application of Euler’s method where, the number of iterations n=2 on the interval 1≤t≤2 and y'=ty with the initial condition y(1)=4.

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Chapter 10.7, Problem 1CYU

Chapter 10.7, Problem 1E

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To graph: The polygonal path corresponding to the application of Euler’s method where, the number of iterations n = 2 on the interval 1 ≤ t ≤ 2 and y ' = t y with the initial condition y ( 1 ) = 4 .

Solution Summary: The author analyzes the polygonal path corresponding to the application of Euler's method where, the number of iterations n=2 on the interval 1le t

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To graph: The polygonal path corresponding to the application of Euler’s method where, the number of iterations n=2 on the interval 1≤t≤2 and y'=ty with the initial condition y(1)=4.

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Chapter 10 Solutions