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August 20th, 2018, 08:48 PM   #1
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First Order Separable Equation Examples

I'm looking for inspiration. I need examples of interesting first order separable equations. If they have a real-life application, that's all the better.
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August 20th, 2018, 09:27 PM   #2
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Population model?
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August 21st, 2018, 02:32 AM   #3
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I have lots, but need some more information on your needs.

Are you more interested in the physics process of developing the model to express the DE
For example

A bacterial polulation P is known to have a rate of growth proportional to P itself.
If the population doubles between 0900and 1000, at what time will the population be 100 times the original?

or the algebraic manipulation for instance

Solve


$\displaystyle \frac{{dy}}{{dx}} = {e^{\left( {2x + 3y} \right)}}$



Practical exmples come from fluid flow, radioactive decay, chemical rates of reaction, population grow, electrical circuits, heat flow, epidemic models, ionisation and recombination and many more.

Indeed anywhere in Physics that we can say the rate is proportional to something else can lead to a separable equation.
Heat flow is interesting because Stefan's Law leads to a non linear separable equation.
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August 21st, 2018, 04:31 AM   #4
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Both. Obviously most algebraic manipulation examples are straightforward to create and solve, although examples such as $1+y'=\frac{y}{x}$ are less obvious.

Applicationwise, and object falling through a resistant fluid (like a parachutist), mixing tank problems (with constant volume) and the most simple population models are the sort of ideas I have, but more would be welcome.

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Originally Posted by studiot View Post
fluid flow, chemical rates of reaction, population grow, electrical circuits, heat flow, epidemic models, ionisation and recombination and many more.
Specific examples of these ideas would be great!

Last edited by v8archie; August 21st, 2018 at 04:44 AM.
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August 21st, 2018, 05:00 AM   #5
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I think I have lost the email address, from last time I sent you a bunch of pages.

Perhaps you could PM it again.

Also still interested in your target audience.
I think my old A level only dealt with simpler ones, some of the applications I mentioend are more difficult, even non linear.
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August 21st, 2018, 07:11 AM   #6
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Target audience is probably A-level, perhaps a touch more. Applications are as much to demonstrate as to set for them. Make it a bit more relevant.
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