Do you know a first orde nonlinear ordinary differential equation in physical process?
Lots of physical situations are represented by nonlinear first order equations (particularly once one moves beyond the simplifications of no friction, air resistance, etc.). Note, however, that the examples of radioactive, decay, Newton’s cooling law, and the charging of a capacitor in an ideal RC circuit given in one of the other answers, are all examples of situations described by *linear* first-order differential equations. (For instance, radioactive decay is described by dN(t)/dt + k*N(t) = 0; all the terms in this equation only involve the dependent variable raised to the 0th or 1st power. Similarly, for Newton’s Law of cooling, dT/dt = -k*(T-Ta), all the terms involve the dependent variable raised to the 0th or 1st power.) Here are two examples of real physical situations described by nonlinear first order differential equations. The differential equation for the velocity as a function of time of a body subject to constant gravitational accelearation and a velocity-dependent drag
