``

a (5, n)uEE + 2B(5, n)uEn + 7(5, n)unn + 6(5, n)us + E(5, n)un + (5, n)u = 0, (2) where a(5, n) = atx + 2beaty + cg2 B(5, n) = aExx + b(Exny + nosy) + csyly, 7 (5, n) = anx + 2bnxy + Cny; 8(5, n) = aExx + 2bExy + cyy + dex + ely, E(5, n) = anxx + 2bnxy + Cnyy + dnx + eny, (5, n) = f (Please do this question before the tutorial. It is repeated applications of the chain rule. A good question to do to understand how the change of variables work, but it is long and fiddly. Too long to do in the tutorial.) b). Show that the coordinate transformation (x, y) = y/x and n = n(x, y) arbitrary, brings the PDE X'uxx + 2xyury + y"ugy + xyur + y'uy = 0 (3 into the form (2) with a = 3 = 6 = 1 =0