Use Euler's Method with three equal step sizes to estimate the value of y(0.3) for the differential equation y ′ = y, with y(0) = 1.

Type your answer in the space below and give 3 decimal places. If your answer is less than 1, place a leading "0" before the decimal point (ex: 0.482).

Note: The last exercise was wrong and I can not understand this method. I'm sure I'm failing something and I do not know. Please can you help me with details I want to understand. Thanks

Why don't you post your calculation, so we can see what's going on? Then we can correct the erroneous steps and show the right way to do it.

It just involves using the tangent line at each step to extrapolate to the next step, using the approximation

∆y = ∆x * dy/dx

That is, it approximates ∆y/∆x using dy/dx.

In case you don't see my update to your previous post, the table should look like:

x......y........y'......∆x......∆y
1.00 1.00 2.00 0.10 0.20
1.10 1.20 2.54 0.10 0.254
1.20 1.454 3.314 0.1 0.331
1.30 1.785
So, (C)

Thanks oobleck I understood the last exercise but in this one how do I know "x" because I have ∆x= 0.35

∆x = 0.35? How is that?

You have y(0) and you want to approximate y(0.3) using 3 steps.
So clearly, ∆x = 0.1 for each step.

It is not affected in any way by the calculations involved. You decide that right at the start.

x........y........y'........∆x......∆y

0 1 1 0.1 0.10
0.1 1.10 1.10 0.1 0.11
0.2 1.21 1.21 0.1 0.12
0.3 1.33 1.33 0.1 0.13

Answer 1.33???

Can you check for me if the answer 1.33 is correct?

woud be "x"= 0, 0.1,0.2,0.3

x......y........y'......∆x......∆y
0 1 1 0.35 0.35
0.1 1.35 1.35 0.35 0.47
0.2 1.82 1.82 0.35 0.63
0.3 2.45 2.45 0.35 0.85

My answer 2.45 but I am not sure. Can you check for me please?