Generally, an individual who is attending college out of state does not intend to abandon their domicile and permanently reside at the location of their college. Thus, students attending college out of state generally are residents of their home state.
If you obtained a driver’s license, obtained in-state tuition, and/or registered to vote in the state where you attend college, then you have likely abandoned your domicile in your home state.
As DE part-year resident, you have to pay income tax on the income earned while you were DE resident. However, you might be able to claim credit on DE return for taxes paid to another state while you were DE resident.