Answer: Bare spots can be patched by loosening the soil, working in some organic matter such as compost, raking it smooth and then seeding. Rake lightly to barely cover most of the seed. Cover with a light layer of straw and water as needed to keep the area moist. Or, use a patch kit and follow the label directions.
If the areas are extensive, you may want to consider removing the existing vegetation and starting from scratch. The best time of year to do this however is late summer to early fall. In preparation for that I would suggest you run some basic soil tests to find out fertility levels and if you need to adjust the pH with lime. This can be done ahead of time.
In the larger area with shade -- and possibly tree roots -- you may find that grass will not grow due to unsuitable condiitons. In this case you may want to consider using a groundcover instead.
Wildflowers or native plants can be a successful choice, however they are not going to be maintenance free. The area will have to be weeded and watered and mulched while they become established, just as with any flowers. Ideally you would select native plants that typically grow wild in your local area. Another option would be to use some long lived relatively low maintenance perennials. For a south or western exposure you could use Hemerocallis, Echinacea purpurea, Sedum, and daffodils. For an east or northern exposure you could use hostas, for example.
Your local county extension should be able to help you with testing your soil and recommending the best grass varieties for your local area, and with deveoping a lawn care and maintenance program. They may also have suggestions as to specific native flowers that do especially well in your local soil and climate.
Enjoy your yard this summer!
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