On bi-quadratic equation with four unknowns 7xy+3z2 = 3w4

Diophantine equations play an important and significant role in Number theory and are numerously rich in variety.. There are several Diophantine equations that have no solutions, trivial solutions, finitely many solutions, and an infinite number of solutions. In particular, we often come across homogeneous and non-homogeneous bi-quadratic equations also.One may require its integral solution in its most general form. Both homogeneous and non-homogeneous Biquadratic equations have aroused the interest of numerous mathematicians since ancient times. Towards this end, this paper concerns with the problem of determining non-trivial integral solutions of the non-homogeneous Biquadratic equation with four unknowns given by 7xy+3z2 = 3w4. We obtain infinitely many non-zero integer solutions of the equation, by introducing the linear transformations x = u+v, y = u−v, z = v