Question

in accounting how can you incorporate the accounting equation to a non-profit organization?

Answer 1

The equity part can be split up into parts to denote where they come from or where they're allocated to (remember, net income goes to the equity side). The terms usually are General Reserves, Operating Reserves, or Special Reserves (if funds were donated for a specific purpose like pertpetual endowments, or capital programs like a building fund.)
You'd see this stated as "Net Assets" or "Fund Balance", and the equation would be Assets equal Liabilities plus Net Assets.