2: Introduction to ODEs
( \newcommand{\kernel}{\mathrm{null}\,}\)
A differential equation is an equation for a function that relates the values of the function to the values of its derivatives. An ordinary differential equation (ode) is a differential equation for a function of a single variable, e.g., x(t), while a partial differential equation (pde) is a differential equation for a function of several variables, e.g., v(x,y,z,t). An ode contains ordinary derivatives and a pde contains partial derivatives. Typically, pde’s are much harder to solve than ode’s.