1. The first question asks to define the complete solution of a partial differential equation (PDE). 2. A complete solution of a PDE is a solution that contains as many arbitrary constants or arbitrary functions as the order of the PDE. It represents the general form of all possible solutions. 3. For example, if a PDE is of order $n$, then its complete solution will involve $n$ arbitrary constants or functions. 4. This is important because it ensures that the solution set is comprehensive and can satisfy a wide range of initial or boundary conditions. 5. In summary, the complete solution of a PDE is the most general solution that includes all particular solutions as special cases.