Linearization of nonlinear system
Linearization can be performed at any point of a smooth curve, as long as the inputs don't perturb the output outside the linearized area.

My way of checking this would just be to simulate it in that range (phase space), and figure out the linear equation around that point. 

Of course take this with a grain of salt. I feel that I've seen the equation for y somewhere before... Can't remember where though (depletion region of MOSFET perhaps..). From just looking at the equations it does not look like you have nonlinear memory effects, so you should be fine. The two first eqns just look like charge accumulation/capacitor differential equations.