In an ordinary differential equation (ODE), we seek a function \(x=x(t)\) in one variable t that solves an equation in which the function x and derivatives of x with respect to t appear. In a partial differential equation (PDE), we seek a function u in several variables, usually \(u = u(x,t)\) or \(u = u(x,y)\) or \(u = u(x,y,z,t)\) , where u satisfies an equation that includes u and partial derivatives of u with respect to the various variables.