[UPSC CSE 1990] Electrostatics and Magnetostatics (Q275, 30M)

The components of an electrostatic field in vacuo are given as E_x = \frac{a}{r^3} + \frac{bx^2}{r^5} E_y = \frac{cxy}{r^5} E_z = \frac{fxz}{r^5} where a,b,c, and f are constants x,y,z, the rectangular cartesian coordinates and r^2=x^2+y^2+z^2. Using the basic equations obeyed by the electrostatic field in vacuo, find he relations between a,b,c and f and determine the charge density at a general point in space. Would that explain the observed field?