Second order partial differential equation Second order partial differential equation:
$$(x-y)^2/4  u_{xx} + (x-y) \sin(x^2+y^2)  u_{xy} + \cos(x^2+y^2)  u_{yy} +\dots=0$$ is
a.  Elliptic in $\{(x,y): x≠y, x^2+y^2<\frac{\pi}{6}\}$
b.  Hyperbolic in $\{(x,y): x≠y, \frac{\pi}{4}<x^2+y^2<\frac{3\pi}{4}\}$
c.  Elliptic in $\{(x,y): x≠y, \frac{\pi}{4}<x^2+y^2<\frac{3\pi}{4}\}$
d.  Hyperbolic in $\{(x,y): x≠y, x^2+y^2<\frac{\pi}{4}\}$
I am stuck on this problem . Can anyone help me please......

compute the expression $S^2-4RT$ . here $S=(x-y)\sin(x^2+y^2)$ , $R=(x-y)^2/4$ , $T=\cos^2(x^2+y^2)$. after calculating we have
$S^2-4RT=(x-y)^2\cos 2(x^2+y^2)$   
so the option ($3$) is correct
