2: Introduction to ODEs
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.