Introducing $x=r\cos{(\theta)}$, $y=r\sin{(\theta)}$ and $$r = \sqrt{x^2+y^2},$$ we can rewrite $$F_{x}=-\frac{GM_{\odot}M_E}{r^2}\cos{(\theta)}=-\frac{GM_{\odot}M_E}{r^3}x,$$ and $$F_{y}=-\frac{GM_{\odot}M_E}{r^2}\sin{(\theta)}=-\frac{GM_{\odot}M_E}{r^3}y,$$ for the $y$ direction.