No. You should not use Schedule E because it is not considered a rental business.
Since your son likely occupies the unit for the entire year at a below-market rate, you effectively have zero days of "fair rental" use for tax purposes.
Instead, you should list the income as "Other Income". Unfortunately, you would not be able to offset your expenses this way.
Your other option is to charge a fair market rent so that you may then use Schedule E.
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