## Question

###### Consider tne following Laplace' equavon(y)-uy(*Y) =0<*<2 D<y<2subject to the given boundary conditionsu(o,y) = u(2y)-Y(2-v), Vy (K,0) = Uy (x,2)=0<Y < 2 0<y < 2 0 <* <2 <<2Given that the general solution of the Laplace' equationMX QX cosh _ B, sinhnaku(xy) = Ag Bo* +Detemmine the values of Aj, Bo A, and B, Hence, vilta tho speclic solullon ulxy) (10 marks}Consider circular nng conditions areinner radiusand outer radius where the boundary0)-100 50cos

Consider tne following Laplace' equavon (y)-uy(*Y) = 0<*<2 D<y<2 subject to the given boundary conditions u(o,y) = u(2y)-Y(2-v), Vy (K,0) = Uy (x,2)= 0<Y < 2 0<y < 2 0 <* <2 <<2 Given that the general solution of the Laplace' equation MX QX cosh _ B, sinh nak u(xy) = Ag Bo* + Detemmine the values of Aj, Bo A, and B, Hence, vilta tho speclic solullon ulxy) (10 marks} Consider circular nng conditions are inner radius and outer radius where the boundary 0)-100 50cos 8 ult 8) = 200, 0<8<21 0 <644 If the gonoral solution E ulc, 8) = Aa Bo Inr + (Ar" B,r-= cosng detemmlne the specfic _ solubon "lcar" Dor sinne_

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