Answer: Planting grass seeds or laying sod won't fix the underlying problem, which is poor drainage. Since it is a rental you probably don't want to install a curtain drain to divert the excess water. So, you might simply want to cover the muddy areas with gravel or river rock and plant colorful flowers in containers that you set on the gravel. If you have your heart set on lawn, you'll need to fix the soil drainage problem first, or at least have some topsoil delivered so you can raise the soil level higher. Once you've done that you can sow grass seeds or lay sod and the grass roots should remain high and dry - and healthy.
Good luck with your landscape!
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