Answer to Question #50904 in Differential Equations for Nayan Jyoti Das

Question

10. a) Find the surface which intersects the surfaces of the system z (x+y) = c (3z+1)
orthogonally and which passes through the circle x^2 + y^2 = 1, z = 1

b) Show that the complete integral of z = px + qy - 2p - 3q represents all possible planes
through the points (2, 3, 0)

c) Find the values of n for which the equation (n-1)^2 uxx - y^2n uyy = ny^2n-1 uy is
i) parabolic ii) hyperbolic.