Advanced Engineering Mathematics: Euler Method

[think4432]

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!

 

[Feldoh]

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?

 

[think4432]

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...

 

[vela]

Hint: What is u' equal to? Rewrite the original differential equation in terms of u.