1. Solve the following first order partial differential equation with an initial condition. 1) ", tuy =, u(2,0) = a +2; u(x,0)=-4x + 1. 2) + uux = 0, 2. Let 2= B (0) be the upper half ball with center at the origin and radius 2. Let 22= B(0) be the upper half ball with center at the origin and radius 3 in R3. Find the harmonic function u(x) inside 2 satisfying the boundary condition: 3 (x 1) + y(x + 1) + (z 1)