Question: Let w (x,y) = In(x 2 + y 2 ). (a) Verify that w (x,y)satisfies the partial differential equation ( 2 w)/ (x 2 )+(

Letw(x,y) = In(x2+ y2).

(a) Verify thatw(x,y)satisfies the partial differential equation

(2w)/ (x2)+(2w)/ (y2)= 0

(b) Suppose thatx = As + Bt,y = As Bt, andA, B 0. LetG(s,t) =

w( x(s, t), y(s,t) ). ComputeG/s and G/ t

(c) Find all pairs of valuesAandBso thatG(s,t) = w( x(s,t), y(s,t) )

satisfies(2G)/ (s2 )+ (2G)/ (t2 )=0

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