Consider the second order PDE au xx + uy = y^2, a E R Select all of the correct statements. Incorrect selections are given negative marks. O The PDE is

always parabolic O The PDE is never hyperbolic O The PDE can be hyperbolic and elliptic but never parabolic O If the coefficient a is replaced by b < O then the PDE is hyperbolic O If the coefficient a is replaced by the function f(x) = e^x then the PDE is elliptic O The PDE is inhomogeneous