## ABSTRACT

Uxx ^ y / yu xy + XMyy + (2x + %j)ux ^ SyUy + 4u = sin (a:2 - 2 y), y > 0,

fits the general form with

A = 1, B = — s/n. C = x, D = 2x + y, E = —3//. F = 4, G = sinf.r2 — 2y),

so B 2 — 4A C = y — 4x. Consequently,

(i) if y > 4x, the equation is hyperbolic;

(ii) if y = 4x, the equation is parabolic;

(iii) if y < 4x, the equation is elliptic.