differential equation

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Some kind of resistive + inductive current divider circuit with interest in two currents
 
excuse me what do u mean exactly? there are two current in a circuit ? a branch common and two current passes through it?
 
electrics said:
excuse me what do u mean exactly? there are two current in a circuit ? a branch common and two current passes through it?
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One way to look at it is to say that there are two parts of the equation with time derivatives. Voltage across an inductor is Ldi/dt. So you could say you have current X and current U. That would make A & B some kind of resistors for the v*i parts of the equation.

if X is i1 and U is i2 and A is R1 and B is R2 and B1 is L2 and an inductor L1 of value 1:

dX/dt=AX +BU +B1dU/dt

L1*di1/dt = R1*i1 + R2*i2 + L2*di2/dt

You can have a part of a circuit that has a common leg shared with some other part of the circuit. You have the left circuit loop with L1 in series with R1 with a loop current of i1 flowing through. This is in series with a shared leg that has loop current i1 plus some loop current i3 from the other part of the circuit. i2 = i1 + i3 flows through the shared leg consisting of the series combination of R2 and L2.
 
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