Don't understand a question on Euler's method on this site's quiz

Hvordan kan vi hjælpe?

Jeffrey Ho

22. april 2024 00:00

I was working on a question on this site about the said theme. I ran into a question that I failed to answer correctly. I looked at the answer and could not comprehend. See the pic below:

dy/dx: 2x+y and y(1)=k

Using Euler’s method, starting at x=1 with a step-size of 0.5, gives the approximation y(1.5)=4.

Find k.

The answer provided has a step on finding the change of y.

F(x,y)*change of x

=F(1,k)*0.5

=(2*1+k)*0.5

=1+0.5k

The question: why =(2*1+k)*0.5?

Nyt opslag

2 kommentarer

J DOG (Josey)

30. april 2024 13:56
1

Kommentarhandlinger Permalink
What kind of math is this 😭 I want to help you (I can learn things very quickly) but I've never done this type of math before
abdulhaq.25.94

11. maj 2026 18:21
0

Kommentarhandlinger Permalink
Euler's method uses the derivative to approximate how much the function changes over a small interval.

Since y'(x) = dy/dx, we can estimate the derivative at x = 1 as:

y'(1) ≈ (y(1.5) - y(1)) / (1.5 - 1)

Substituting the given values:

y'(1) ≈ (4 - k) / 0.5

We also know from the differential equation that:

y'(x) = 2x + y

At x = 1, y = k, so:

y'(1) = 2(1) + k = 2 + k

Now set the two expressions equal:

2 + k = (4 - k) / 0.5 = 8 - 2k

3k = 6

k = 2

This is why the solution uses F(1, k) = 2(1) + k. We substitute x = 1 and y = k into the formula y' = 2x + y.

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Don't understand a question on Euler's method on this site's quiz

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2 kommentarer

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