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November 20th, 2007, 03:35 AM   #1
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differential equation problem

Hi, I am trying to solve the following differential equation:

df(t)/dt = A*g(t) - D*f(t)

where 'A' is a (positive) constant and

D = B*g(t->infinity)/f(t->infinity) + C

where 'B' and 'C' are constants (positive). The initial condition is f(0) = 0.
The obvious problem is that the constant(?) 'D' is dependent on f, so in order to solve the equation 'D' must be known, but that requires in turn that f(t->infinity) is known. g(t) is continous (but its derivative may not be continous everywhere) and g(t)->0 when t->infinity (so f(t)->0 when t->infinity, but the limit g(t)/f(t) exists when t->infinity).

I suppose that this problem has to be solved with numerical methods (iteration), but there is perhaps also an analytical solution to this problem. Maybe there is some standard method for this kind of problem? I would be grateful for any advice on how to solve this, analytically or numerically.

Best regard,

Mattias
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