Solving IVP with Euler's Method: Step Size h = 0.1

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Discussion Overview

The discussion revolves around using Euler's method to find an approximate solution to an initial value problem (IVP) defined by the differential equation \(\frac{dy}{dx} = 4xy + 3\) with the initial condition \(y(0) = 0\). The focus is on determining the appropriate function \(f(x,y)\) for the method.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant seeks clarification on whether the function \(f(x,y)\) for the given IVP is simply \(4xy + 3\).
  • Another participant confirms that \(f(x,y) = 4xy + 3\) is indeed correct.
  • A third participant expresses appreciation for the confirmation received.
  • A later reply implies a light-hearted expectation for deeper consideration of the problem following the confirmation.

Areas of Agreement / Disagreement

Participants generally agree on the identification of \(f(x,y)\) as \(4xy + 3\), but the discussion does not delve into further complexities or alternative approaches.

Contextual Notes

The discussion does not address potential limitations or assumptions related to the application of Euler's method or the specific characteristics of the IVP.

Ed Aboud
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Hi all.

Could someone give me a hand with this:

Using Euler's method find an approximate solution to the IVP using step size h = 0.1

[tex]\frac{dy}{dx} = 4xy + 3[/tex] , [tex]y(0)=0[/tex]

I know how to use Euler's method for something simple like [tex]\frac{dy}{dx} = x + y[/tex]
But I'm just not to sure what to take as the [tex]f(x,y)[/tex].

Is it just simply [tex]f(x,y) = 4xy + 3[/tex]

Thanks for any help.
 
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Ed Aboud said:
Is it just simply [tex]f(x,y) = 4xy + 3[/tex]
Yes.
 
Ok cool.
Thanks for the help!
 
I assume that since the answer was "yes", you will give it the most thought!
 
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