Chapter 1.1, Problem 4E

In Problems 1 - 12, a differential equation is given along with the field or problem area in which it arises. Classify each as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independence and dependent variable. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear.

$\frac{{\partial }^{2}u}{\partial x^2}+\frac{{\partial }^{2}u}{\partial y^2}=0$

(Laplace’s equation, potential theory, electricity, heat, aerodynamics)