Any homeopathic way to get rid of dandelions?

My back yard is absolutely covered in dandelions. They are not the short-stemmed kind with the large flowers, but the long stemmed kind with the small flowers. They are invasive, and grow so much faster than the grass, I have to practically mow my lawn every three or four days to keep them from over-running us. (I fell behind, and am now overrun!)

Going out and buying a professional product (like Weed’n’Feed) would cost entirely too much for the area I need to treat, so I was wondering – is there anything I can mix up at home that would effectively kill the weeds without harming my grass?