Explanation Given information: y ' = g ( t , y ) = t y where 1 ≤ t ≤ 2 with the initial condition y ( 1 ) = 4 . 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 ) =

12th Edition

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 1CYU

To determine

To calculate: The approximate solution f(t) to y'=ty with the initial condition y(1)=4 using Euler’s method with number of iterations n=2 on the interval 1≤t≤2 and then find the value of f(2).

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Chapter 10.6, Problem 25E

Chapter 10.7, Problem 2CYU

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The approximate solution f ( t ) to y ' = t y with the initial condition y ( 1 ) = 4 using Euler’s method with number of iterations n = 2 on the interval 1 ≤ t ≤ 2 and then find the value of f ( 2 ) .

Solution Summary: The author calculates the value of f(2) by using Euler's method with number of iterations with the initial condition.

To calculate: The approximate solution f(t) to y'=ty with the initial condition y(1)=4 using Euler’s method with number of iterations n=2 on the interval 1≤t≤2 and then find the value of f(2).

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Chapter 10 Solutions