Why not separable (basic question)?

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Discussion Overview

The discussion revolves around the separability of the first-order ordinary differential equation (ODE) given by y' + 2xy = x, as presented in a textbook. Participants explore whether the equation can be separated into a form that allows for integration, with some seeking clarification on the author's assertion that it is not separable.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant presents a method to separate the equation, suggesting that dy/(1-2y) = xdx is a valid transformation.
  • Another participant questions the author's claim, indicating that they do not see any issues with the separation process.
  • A third participant confirms the equation is indeed as stated and challenges the author's assertion that it is "plainly" not separable.
  • A later reply mentions that the author acknowledged a mistake, indicating the equation is separable after all.

Areas of Agreement / Disagreement

Participants express disagreement regarding the author's claim about the equation's separability. While some participants argue it can be separated, the initial assertion from the author that it is not separable is contested. The discussion reflects multiple viewpoints without a clear consensus on the author's original statement.

Contextual Notes

There is uncertainty regarding the validity of the separation method used by the first participant, as they seek help in identifying any mistakes. The discussion also highlights a potential miscommunication or error in the author's text.

jla2w
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In Example 1.5 of Differential Equations Demystified, the equation is y' +2xy = x, and the author claims this is not separable. Now, what am I missing. I try the following.

1) dy/dx = x - 2xy
2) dy/dx = x(1-2y)
3) dy/(1-2y) = xdx

I guess one of those is invalid but I just cannot identify which. Any help appreciated, thanks. This is part of an effort to brush up on ODE since it's been years since I took it and now I'm going for a Master's in Applied Math, need lots of help of this kind. Thanks
 
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Hmm, are you sure that's the equation they gave? I don't see what's wrong with that.
 
Yes, that's definitely the equation, and the author says
"This equation is plainly not separable (try and convince yourself that this is so)."
 
Last edited:
Maybe it isn't separable but I don't see how it's "plainly" not separable, you seem to agree
You just separated it, disproving the author's claim.
 
Author wrote me back saying that it was a mistake, so that is in fact a separable equation.
 

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