1. Consider the PDE Ux + yuy = V1 u? on R. (a) Is the PDE linear or nonlinear? What is its order? (1 points) (b) Write down the full set of characteristic equations for this PDE and sketch a few characteristic curves in the xy-plane. (3 points) (c) Solve the PDE with the auxiliary condition u(0, y) = sin y. (6 points). 1. Consider the PDE Ux + yuy = V1 u? on R. (a) Is the PDE linear or nonlinear? What is its order? (1 points) (b) Write down the full set of characteristic equations for this PDE and sketch a few characteristic curves in the xy-plane. (3 points) (c) Solve the PDE with the auxiliary condition u(0, y) = sin y. (6 points).