Consider the following PDE on the first quadrant U = {($1, 12)|x1 > 0, 12 > 0}: Ur, Uxz - us = 0 on U u = 1 at OU (a) Is this PDE linear, semilinear, quasilinear or fully nonlinear? (b) Show that this PDE is equivariant under the dilation scaling (ZA, bu)($1, 12) = X+lu(Xx1, X.x2) where A * 0 and A, b ER. (c) Derive an ODE for solutions invariant under the scaling Zx,-1- (d) Solve the ODE of part (c) and give the corresponding solution to the PDE. Varify that you can match the boundary conditions. (e) Repeat steps (c) (d) for the scaling Zx,1. Does it give you different solutions