Find the general solution of the equation r + 4t = 8xy , by Monge's method. Find also the particular solution for which 2 z = y and p = 0 ,

Find the general solution of the equation r + 4t = 8xy Find also the particular solution for which z = y2 and p = 0 when x = 0. Solution: Homogeneous solution 1 r + 4t = (D2 + 4(D0)2) zh = (iD + 2D0)(?iD + 2D0) zh = 0 Hence zh = f(2ix + y) + g(?2ix + y) + cc where f and g are some arbitrary complex