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.
