How can I fix my patch lawn?

Ryan180680

after such a wet winter my lawn has quite a few bare muddy patches around the edges but also from where the dogs have walked on it. Is it best to rake the affected areas then sow seed and add a layer of compost? Also is there a quicker way to germinate? I've heard that using polythene helps? 

Ryan180680

Brilliant thanks very much. I might hold off a week or two as the forecast doesn't look great with possibility of frost