Explain the answers please

18. The solution of Laplace's equation Urr + -Ur + -10e = 0 within the circler = 2, which satisfies the boundary condition u(2, 0) = 2 - 3 sin(20) + 2 cos(30), is u(r, 0 ) = ao + 2 rn an cos(no) + bn sin(no) , where n=1 (a) do = 4, b2 = -3, a3 = 2, an = bn =0 otherwise (b) do = 4, a2 = -3, b3 = 2, an = bn = 0 otherwise (c) do = 4, a2 = -- b3 = -, an = bn = 0 otherwise 4 H (d) do = 4, b2 = - a3 - 4 an = bn = 0 otherwise (e) None of these 19. The differential equation xy" + 3y' -ry + Ax?y =0, when placed in the Sturm-Liouville form [p(x)y'' - q(x)y + Ar(x)y = 0, has the weight function r(x) = (a) 23 (b) x4 (c) 25 (d) x2 3x (e) None of these