Shady, hilly side yard erosion.
You will want to plant things that have deep roots and can tolerate shade. For example a frequent shade plant, Hosta, has very shallow roots. Small shrubs or trees could work. Mulching will also help hold the soil in place.. The following website gives our recommendations. A soil test would also help to determine what will grow well. See: https://extension.umn.edu/planting-and-growing-guides/gardening-shade. Also see: http://soiltest.cfans.umn.edu/