- #1
zeroseven
- 16
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Hi everyone, new member zeroseven here. First, I want to say that it's great to have a forum like this! Looking forward to participating in the discussion.
Anyway, I need to solve a pair of differential equations for an initial value problem, but am not sure if an analytical solution exists. I have been able to solve a special case as I explain below, but remain stumped with the more general form.
The equations are as follows:
dx/dt=-ax-cxy
dy/dt=-bx-cxy
Where a, b, and c are constants (all >0 in the problem I am trying to solve) and x and y the functions I need to solve.
I can solve the special case when a=b by substracting the 2nd eq. from the 1st. Then I get
d(x-y)/dy=-a(x-y) which is easy to solve for x-y, and the rest is pretty easy too. But this doesn't work for the general form where a and b are different.
Anyone have any ideas? Ultimately, what I really need is x*y, so if there is a way to get that without solving for x and y first, that is fine too.
They look deceptively simple, I hope a solution exists!
Cheers,
zeroseven
Anyway, I need to solve a pair of differential equations for an initial value problem, but am not sure if an analytical solution exists. I have been able to solve a special case as I explain below, but remain stumped with the more general form.
The equations are as follows:
dx/dt=-ax-cxy
dy/dt=-bx-cxy
Where a, b, and c are constants (all >0 in the problem I am trying to solve) and x and y the functions I need to solve.
I can solve the special case when a=b by substracting the 2nd eq. from the 1st. Then I get
d(x-y)/dy=-a(x-y) which is easy to solve for x-y, and the rest is pretty easy too. But this doesn't work for the general form where a and b are different.
Anyone have any ideas? Ultimately, what I really need is x*y, so if there is a way to get that without solving for x and y first, that is fine too.
They look deceptively simple, I hope a solution exists!
Cheers,
zeroseven
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