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 ) =

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

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

Publisher: PEARSON

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Question

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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Chapter 10 Solutions

Calculus & Its Applications (14th Edition)

Ch. 10.1 - Show that any function of the form y=Aet3/3, where...Ch. 10.1 - If the function f(t) is a solution of the...Ch. 10.1 - Prob. 3CYU Ch. 10.1 - Show that the function f(t)=32et212 is a solution...Ch. 10.1 - Show that the function f(t)=t212 is a solution of...Ch. 10.1 - Show that the function f(t)=5e2t satisfies...Ch. 10.1 - Show that the function f(t)=(et+1)1 satisfies...Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Is the constant function f(t)=3 a solution of the...

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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