in Exercises 3.6, for some problems you will

Chapter 3, Problem 7E

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QUESTION:

in Exercises 3.6, for some problems you will find it essential to have a calculator or computer available.† For 1–17, note whether or not is bounded.Use the fourth-order Runge–Kutta subroutine with h = 0.25 to approximate the solution to the initial value problem at x = 1. (Thus, input N = 4.) Compare this approximation to the actual solution y = 3 -2e2x evaluatedat x = 1.

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QUESTION:

in Exercises 3.6, for some problems you will find it essential to have a calculator or computer available.† For 1–17, note whether or not is bounded.Use the fourth-order Runge–Kutta subroutine with h = 0.25 to approximate the solution to the initial value problem at x = 1. (Thus, input N = 4.) Compare this approximation to the actual solution y = 3 -2e2x evaluatedat x = 1.

ANSWER:

Solution:Step-1:In this problem we need to approximate the solution to the initial value problem at x = 1 by using the fourth-order Runge kutta subroutine with h = 0.25 and we have to compare this approximation to the actual solution .Step-2:Given: We know that, the fourth-order Runge kutta subroutine approximation formula is:Where , We know that at x = 0 , then the value of y is one.So,initial value of y is one..If h = 0, then the val

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