A differential equation is termed as an ordinary differential equation, abbreviated through odes, if this has ordinary derivatives in it. Similarly, a differential equation is termed as a partial differential equation, abbreviated through pde, if this has differential derivatives in it. In the differential equations as in above equation (3) - equation (7) is odes and equation (8) - equation (10) is pde's.
The huge majority of these notes will deal along with odes. The only exception to that will be the last section wherein we'll acquire a brief look at a general and basic solution technique for resolving pde's.