How do I prove the following inequality :
$$\Bigg(\frac{2}{\alpha^2} \, \big( e^{\alpha x} - e^{\alpha y} \big) \, + \, e^{\alpha y} (y^2 - x^2) \; \Bigg) > 0 $$
given, $x, y > 0$ ?
Can anyone provide me with hints about this problem ?
Thanks in advance.
Here, $\alpha$ is a positive constant.