(a) If u(x,y) = sin(2x^2 + y) is a solution of the partial differential equation
∂^2u/∂x^2 + 8∂^2u/∂x∂y + a∂u/∂x + b∂u/∂y + 2∂u/∂y∂x + 8∂^2u/∂y^2 = 0
at all points (x,y) on the Oxy plane, find the values of the constants a and b.
(b) Apply the method of separation of variables on the partial differential equation
∂v/∂x + (1+x^2+y)v∂v/∂x = 0
to obtain a pair of ordinary differential equations having an arbitrary constant in them. (Let w(x,y) = X(x)Y(y)). Do not attempt to solve the ordinary differential equations you obtain.