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Euler’s Method Let’s get our hands dirty and actually use Euler’s method to estimate the value...

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Advance Math

Euler’s Method Let’s get our hands dirty and actually useEuler’s method to estimate the value of y(2) where y is thesolution to the initial value problem

y?=y?2x            y(0)= 1

Recall that Euler’s method says: Approximate values for thesolution of the initial value problem

y?=F(x, y),y(x0) =y0 with step size h, at xn=xn?1+h, are

yn=yn?1+hF(xn?1, yn?1)

Fill in the table for steps of size h= 0.2.

nxnyn=yn-1+0.2F(xn-1,Yn-1y'=F(xn,yn)
001
1

.2

2.4
3
4
5
6
7
8
9
10

Graph the portion of the approximate solution curve you foundabove. It should look like a lot of line segments. The firstsegment has been given on the grid below:

(c) Suppose f(x) is an exact solution to the initial valueproblem above. Describe, with justification, the behavior off(x) asx??. Hint: Graphing a slope field may be helpful for this.

Answer & Explanation Solved by verified expert
4.4 Ratings (916 Votes)
h 0200000000000000ntnyEulerdydx0 0000000 1000000 10000001 0200000 1200000    See Answer
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