Differential Equations:

F(t, y, dy/dt,....,dny/dtn) = 0;  

this is an nth order ordinary differential equation.  The order of a differential equation is the difference between its highest and lowest orders within the equation (with y being a zeroth order derivative). Consider

dy/dt + y = 0;  this is a first order differential equation.

d2y/dt2 + dy/dt + y = 0; this is a second order.

for Example 1:

for Example 2:

for compartmental kinetics example