Use techniques from $18.2 to show that the equation + xuy = Inx is
Classify the equation xuzz - (sinz)ugy = I + y defined over -00 < I < 00 and
-00 < y < 00, as elliptic, parabolic, or hyperbolic. If the equation is of mixed type,
identify the relevant regions and give the classification within each region.
Decide whether each equation can be solved using the method of separation of
variables by testing whether the variables in a product solution X [(x)T(t) can be
separated. Assume that A, B, and C are positive constants. Do not solve the
(a) Auzz + Buz + = u
(b) Auz + Buxt + Cun = u
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