ABSTRACT
In this section we set out a method of finding solutions of linear partial differential equations of the first order. We start by considering a particular example, namely
2 ∂u
∂x + 3
∂u
∂y = 0. (10.1.1)
Associated with this are certain curves in the (x, y)-plane specified by obliging them to have the slope which satisfies
dy
dx =
2 , (10.1.2)
the right-hand side being the ratio of the coefficients of the two partial derivatives in (10.1.1). The general solution of (10.1.2) is y = 32x + C where C is a constant and the curves are, in fact, straight lines. They are drawn for various values of C in Figure 10.1.1. These special curves are known as the characteristics of the partial differential equation (10.1.1).
