Use Euler's method with step size 0.2 to estimate y(1.4), where y(x) is the solution of the initial-value problem y'=x-xy, y(1)=0
$$y_1=0.2$$
$$y_2=0.392$$
$$y_3=0.56224$$
$$y_4=0.70232$$

Question

Use Euler's method with step size 0.2 to estimate y(1.4), where y(x) is the solution of the initial-value problem y'=x-xy, y(1)=0
$$y_1=0.2$$
$$y_2=0.392$$
$$y_3=0.56224$$
$$y_4=0.70232$$

anonymous · Answer

Do I continue until the numbers stop changing or can I stop at y(1.4)?

anonymous · Answer

It's only asking you to approximate y(1.4) so you don't need to go any further.

anonymous · Answer

Thank you sir.

anonymous · Answer

What x value did you begin at? 1. At a step size of .2, that means I'll need to do two steps to get to 1.4

anonymous · Answer

Correct. My x0=1. I don't know why I added a 4th line. Sry

anonymous · Answer

You actually don't even need the third line.

anonymous · Answer

Yes I do.
$$0+0.2(1-0)=0.2$$
$$0.2+0.2(1.2-(0.2)(1.2))=0.392$$
$$0.392+0.2(1.4-(1.4)(0.392))=0.56224$$

anonymous · Answer

I'm pretty confident that you don't.
You KNOW the y value when x is 1. That's given.
Your step size is .2, and each time you do your fancy-pants calculation, it gives you an approximation for what y is when x is .2 higher than before.

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