This paper deals with the quartic Diophantine equation \(X^4-Y^4=R^2-S^2\) . We solve this equation using four suitable linear transformations to get a non-trivial integer solution. In the first transformation, we consider \(X=px+u, Y=qx-u, R=x+v, S=px+v\) . In the second transformation, replace \(S=px+v\) by \(S=px-v\) while maintaining the other transformation as in the previous transformation. In the third transformation, we have used the \(X=v, Y=px+v, R=qx+u, S=x+u\) . In the final transformation, we deploy the transformation \(X=-v, Y=px-v, R=qx-u, S=x+u\) , and obtain infinitely many integer solutions through the parametric method.
