analytic solution of an iterative equations

Hello, my question is about a unique solution of nonlinear iterative function in Matlab, to be more clear the function that I am looking for is function of time which is initial 0

if true
f(t=0)=0
f'(t)=A/B                % is known, 
(A-k.*f(t))/B.*t = f(t)  %here A, B k is also known 
f(t)=A/B.*t       %f(t) is linear function of time 't' without k, but in actual case k exists              
end

for variables A,B,k, I want to find out specific time when f(t)=2, with respect to known parameters, thanks for any suggestions in advance...

[Metin]

I have written wrong, sorry initial value of

    %f'(t=0)=A/B;

here the starting slope is known but due to k.*f(t), the slope of f(t) is also time dependent, good night

[Walter Roberson]

So this could be written as

f(0) = 0
f' = A/B for constant A/B

? If so then f(t) = A/B * t + C for some constant C and f(0) = 0 ensures the constant is 0, leaving f(t) = A/B * t

but then that would seem to contradict your use of k unless k = 0 ??

[Walter Roberson]

To get the expression involving k to work,

f(t) = A*B/(k*t+B)^2

which simplifies to f(t) = A/B when k is 0 -- which is different than f'(t) = A/B . Perhaps you wanted

(A-k.*f(t))/B.*t = f'(t)

[Metin]

Hi, in fact no,

    (A-k.*f(t))/B.*t = f(t)

is right, question arises to calculate power losses of a mosfet in conduction mode, here mosfet on state resistance value is constant k, but during on state current is a linear function of time such

    f(t)=A/B.*t

without voltage drop on mosfet, but as voltage drop is also function of current (time), which is:

     k.*f(t)

for that reason current is not actually linear any more by the time it is increasing, but the voltage drop on mosfet as well, in simulink with feedback it is easy to find out time needed to reach a specific value of current but I have to calculate rise time in matlab m.file,that is reason trying to solve such problem, thanks for comment