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**bugatti79** a) Determine whether the given eqn is hyperbolic, parabolic or elliptic

b) Determine the subset of R^2

c) Determine the characteristics curves

$\displaystyle

u_{xx}+2xu_{yx}+u_{yy}+Cos(xy)u_{y}=u(x,y)

$

$\displaystyle

B^2-AC = x^2-1(1) = x^2-1

$

a)

Hyperbolic if $\displaystyle x^2-1 > 0 $

ie $\displaystyle x^2>1 $

$\displaystyle

x>1, x<-1

$

Elliptic if $\displaystyle x^2-1< 0$

ie $\displaystyle x^2< 1 $

$\displaystyle

-1<x<1

$

Parabolic if $\displaystyle x^2-1 = 0$

ie $\displaystyle x^2=1 $

$\displaystyle

x=-1, x=+1

$

b) How do you write the subset query correctly?