What is the difference between ordinary differential equations and partial differential equations?

partial differential equations deal with functions having more than one variable, so you have to deal with each variable separately, or presume a fixed condition for one of the variables so that you have an ordinary differential. Pressure and temperature will act in their own particular ways during a chemical reaction, say, so trying to figure out where the equilibrium condition lies requires considering the effects of each, separately.

ODE-Ordinary differential equation

differential equations involving one or more functions of one independent variable and their derivatives (like x+sinx)

PDE-partial differential equation

contain one or more functions of multiple variables (like x+Y)