Diophantine analysis

For non-zero integer solutions of the given equation we have to have $x^2$ in the form $a^2-b^2$ , $y^2$ must be in the form $2ab$ . This implies that $a$ and $b$ must be of the form $2m^2(2n+1)$ and $2n+1$ respectively. Here $a, b, m, n$ are all integers. Then $a^2-b^2=(2n+1)^2(4m^4-1)$ . Since $4m^4-1$ in never a square for any integer value of $m$ , the given equation has no integer solutions