Forming PDE by eliminating arbitrary constant
To form a partial differential equation (PDE) by eliminating arbitrary constants, first, differentiate the given equation partially with respect to each independent variable, introducing new terms like p (∂z/∂x) and q (∂z/∂y). Then, use these resulting derivative equations to solve for the arbitrary constants. Finally, substitute these solved values back into the original equation to obtain the PDE, where the number of derivatives taken equals the number of independent variables, and the number of derivatives taken equals the number of arbitrary constants to get a first-order PDE.