12) Problem 12Solve haplace is equationj²u²-2 (124) + 1/2 806²=0arfor U (r, o) on the half-disc04542, 0204111with boun daryConditionsU₂ (₁0) = 0 and Up (v₁TT) = 0=0drez andforU (2₁0) = f(0)for OEGET, where fro) is a givenfunition. You may assume that uis bounded near r=0 Ans.U (₁,0) = A+An =Σ An r² (s(no)nzjAo = = ₁ So flor doयाIT2²/10 So ² Ble) conede. 1=1,2,

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Problem 12 Selve haplace is equation +31 (124) + 1/2 3/4 u for 1 (1₁0) on the half-disc 04542, Conditions le(re) = 0 and Up (r₁TT) = 0 derez and 44, with boun dary for U (2₁0) = f(o) for OSBETI, where f(o) is a given function. You may assume that u is bounded near r=0