Question: 1 (Change of Coordinates) 6P. For this problem we will consider the following linear PDE 12 u + dy 2 x , y ER. (1) (a) By making the change of variable r = (x2 + y?) /2 find a solution for (1) in terms of r by first reducing it to an ODE. For what values of r is the solution defined? (3P.) Rewrite the solution in terms of a and y and verify that it indeed solves (1). (b) Let O be the rotation matrix defined by (3P.) 0 = cos 0 - sin 0 sin 0 cos0 Recall that O defines a rotation by the angle 0 in R2. Show that if u(x, y) is a solution to (1) then as2 + at2 = 0, where s and t are given by O