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May 5th, 2013, 11:47 AM   #1
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solution to this differential equation

Hi. Working in a research project, we came along this set of coupled differential equations:

S1 = (p1 + q11 Y1 + q12 Y2) (1 ? Y1 ? Y2)
S2 = (p2 + q22 Y2 + q21 Y1) (1 ? Y1 ? Y2)

where S1 and S2 are the derivative functions with respect to time of Y1 and Y2 respectively.
p1, p2, q11, q22, q12 and q21 are all constants of the model.

Are math skills are limited. Can you help us solve this set of equations (if possible)?

Thanks a lot!!
jazz_1969 is offline  
 
May 5th, 2013, 03:24 PM   #2
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Re: solution to this differential equation

Hello, jazz_1969!

Quote:
Working in a research project, we came along this set of coupled differential equations:

[color=beige]. . [/color]S1 = (p1 + q11Y1 + q12Y2) (1 ? Y1 ? Y2)
[color=beige]. . [/color]S2 = (p2 + q22Y2 + q21Y1) (1 ? Y1 ? Y2)

where S1 and S2 are the derivative functions with respect to time of Y1 and Y2 respectively.
p1, p2, q11, q22, q12 and q21 are all constants of the model.

Our math skills are limited.
Can you help us solve this set of equations (if possible)?

All those subscripts are dazzling and blinding.

Let's make some substitutions:

[color=beige]. . [/color]

Then we have:[color=beige] .[/color]


Maybe someone is willing to work on it now . . .

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May 5th, 2013, 08:52 PM   #3
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Re: solution to this differential equation

hehe... thank you soroban!
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