1. **Problem Statement:** Define a PDE and give an example of a linear PDE of order 2. 2. **Definition:** A Partial Differential Equation (PDE) is an equation involving partial derivatives of a function of several independent variables. 3. **Example:** A linear PDE of order 2 is the heat equation: $$u_t = k u_{xx}$$ where $u$ is the unknown function, $t$ is time, $x$ is space, and $k$ is a constant. 4. **Explanation:** The order of a PDE is the highest order of derivative present. A PDE is linear if the unknown function and its derivatives appear to the power 1 and are not multiplied together. Final answer: A PDE is an equation involving partial derivatives of a function of multiple variables. An example of a linear PDE of order 2 is $$u_t = k u_{xx}$$.