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1 Use techniques from $18.2 to show that the equation + xuy = Inx is linear. 2 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. 3 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 equation. (a) Auzz + Buz + = u (b) Auz + Buxt + Cun = u

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