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RE:How to set up a diff equation for circuit with a diode?

The equation commes from the physics of a p-n junction. The 0.026 in front is really k*T/q, k== Boltzmann's constant, T is temperature in kelvin, q is the electronic charge.

The 10^12 inside is a function of the area ans structure of the diode. it can be thought of as also the reverse leakage current. It changes dramatically with temperature (~ proportional to T^3/2).

Of course there are many reasons why real diodes deviate from this formula. 

series resistance will make higher by I*Rseries. At very low and very high currents, the ln[] function gets modified.

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