Find u(x,y) harmonic in the region in the first quadrant bounded by y = 0 and...

Find u(x,y) harmonic in the region in the first quadrant bounded by y = 0 and y = √3 x such that u(x, 0) = 13 for all x and u(x,y) = 7 if y = √3 x . Express your answer in a form appropriate for a real variable problem.

Expert Solution

Tuesday 25. JUNE 19 two thousand nineteen Week - 26th 176-189 To Find u(x,y) harmonic in the 1st Appointment quadrant bounded by yzo and y=13x such that u(x,0) = 13 2=(xv) u (x, y) = 7 if y= √3x consider the harmonic function Arg (2) Applying given conditions Ux,0) = Argos Arg (x,0) + 7 = 0+ 7 = 7 u(x,y) = 13 where y =/3 x Arg (x,y) = 7 :. fulx,y) = 18 Arg (a.y) +7 we see that UlXro) = vlxly) = 18 Arg (0) +7=7_ 18 (Arg (x, [3x)2 47 = 18 17 +7= 13 T3 Scanned with CamScanner

Colby Messinger answered 2 hours ago

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