Advanced Engineering Mathematics: Euler Method

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The discussion focuses on solving the differential equation y' = (y - x)² with the initial condition y(0) = 0 using the Euler method. While the problem suggests performing 10 steps, participants argue that 3-4 steps may be sufficient for an approximate solution. There is confusion regarding obtaining the exact solution, with emphasis on rewriting the equation in terms of u = (y - x) to facilitate understanding. The conversation also touches on the potential to estimate error using Taylor series, although some participants note that this topic may not be part of their current curriculum. Ultimately, the differential equation can be solved, despite its non-linear nature.
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Do 10 steps. Solve the problem exactly. Compute the error (Show all details).

The problems says do 10 steps, but 3-4 steps will suffice!

Problem: y(prime) = (y-x)^2
y(0) = 0
h = 0.1

I don't understand how to get the exact solution and what to do from there!
I know that,
f(x,y) = (y-x)^2

And that u = (y-x)

But from there, I am stuck!

Help!
 
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The differential equation can be solved. However it's not a very obvious solution since it is not linear.

However you can get a bound on the error if you think about the problem in terms of Taylor series. Specifically what's the difference in using Euler's method versus a Taylor series?
 
Feldoh said:
The differential equation can be solved. However it's not a very obvious solution since it is not linear.

However you can get a bound on the error if you think about the problem in terms of Taylor series. Specifically what's the difference in using Euler's method versus a Taylor series?

I don't think we're learning about Taylor series, but I just don't understand how we would solve the DE...

I can probably apply to Euler's method after solving it...
 
Hint: What is u' equal to? Rewrite the original differential equation in terms of u.
 

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