Classification of Partial Differential Equations

For analyzing the equations for fluid flow problems, it is convenient to consider the case of a second-order differential equation given in the general form as

(1.1)

If the coefficients A, B, C, D, E, and F are either constants or functions of only (x, y) (do not contain or its derivatives), it is said to be a linear equation; otherwise it is a non-linear equation.

An important subclass of non-linear equations is quasilinear equations.

In this case, the coefficients may contain or its first derivative but not the second (highest) derivative.

If the aforesaid equation is homogeneous, otherwise it is non-homogeneous.