I am trying to find a (smooth, if possible) homeomorphism between $\mathbb{R}\_+ \times \mathbb{R}\_+$ and $\mathbb{R}\_+ \times \mathbb{R}$. i have come with some ideas, but the resulting functions are somewhat complicated. Is there a "simple-equation" homeomorphism between these two spaces ?

Thanks a lot for your help and suggestions !!!

Greetings