Let f(x, y) = x/y. We let x = 0.1 and yo = 3 and pick a step size…

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Let f(x, y) = x¹/y.

We let x = 0.1 and yo = 3 and pick a step size h = 0.2. Euler’s method is the the following algorithm. From in and yn, our approximations to the solution of the differential equation at th

next stage by computing

Xn+1 = xn+h,

Complete the following table. Your answers should be accurate to at least seven decimal places.

Yn

3

n

0

1

2

3

4

In

0.1

The exact solution can also be found using separation of variables. It is

y(x) =

=

Thus the actual value of the function at the point x = 1.1

y(1.1)

Yn+1 = Yn+h. f(xn, Yn).

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