Explanation Given information: y ' = g ( t , y ) = t − 2 y where 2 ≤ t ≤ 3 with the initial condition y ( 2 ) = 3 . Formula used: The endpoints ( t 0 , y 0 ) , ( t 1 , y 1 ) , ... , ( t n , y n ) of the line segments approximating the solution of the equation y ' = g ( t , y ) y ( a ) = y 0 on the interval a ≤ t ≤ b are given by the following formulas: t 0 = a , y 0 t 1 = t 0 + h , y 1 = y 0 + g ( t 0 , y 0 ) ⋅ h t 2 = t 1 + h , y 2 = y 1 + g ( t 1 , y 1 ) ⋅ h . t n = t n − 1 + h , y n = y n − 1 + g ( t n − 1 , y n − 1 ) ⋅ h Where, h = b − a n : Calculation: Here, g ( t , y ) = t − 2 y , a = 2 ,

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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 6E

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To calculate: The approximate solution f(t) to y'=t−2y with the initial condition y(2)=3 using Euler’s method with number of iterations n=2 on the interval 2≤t≤3 and then find the value of f(3)

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Chapter 10.7, Problem 5E

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The approximate solution f ( t ) to y ' = t − 2 y with the initial condition y ( 2 ) = 3 using Euler’s method with number of iterations n = 2 on the interval 2 ≤ t ≤ 3 and then find the value of f ( 3 )

Solution Summary: The author calculates the value of f(3) by using Euler’s method with number of iterations.

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To calculate: The approximate solution f(t) to y'=t−2y with the initial condition y(2)=3 using Euler’s method with number of iterations n=2 on the interval 2≤t≤3 and then find the value of f(3)

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Chapter 10 Solutions