Problem 1E

Problem

As in Exercises 3.6, for some problems you will find it essential to have a calculator or computer available.† For Problems 1–17, note whether or not is bounded.

Determine the recursive formulas for the Taylor method of order 2 for the initial value problem

Step 1</p>

In this problem we have to determine the recursive formula for the Taylor method of order 2 for the initial value problem

, .

Recursive formula for the Taylor method of order is given by,

.

.

Step 2</p>

We have

Now we need to calculate

so,

And,

Therefore .

Or,

Hence, .