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.(adsbygoogle = window.adsbygoogle || []).push({});

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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# Solving a pair of nonlinear coupled DEs

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