Uxxuyy 0uc 2costhetasinthetawhere c x y x2 y2 4 is the

Question

let omiga be the disk of radius 2: omiga :{(x,y): x^2+y^2<=4} solve the Laplace equation:

Uxx+Uyy= 0
U|C = 2(cos(theta)+sin(theta))
Where C: {( x, y)} :x^2 +y^2 =4} is the circle of radius 2 centered at the origin. Can u express the solution U as a function of x and y?