1. Algebraic or polynomial: identify by degree: 1. Linear; 2. Quadratic; 3. Cubic; 4. Quartic; 5. Quantic
2. Transcendental (not polynomial)
3. Diophantine (must be integers)
4. Parametric
5. Functional
6. Differential
7. Integral (latter two can be combined)
8. Difference
9. Identity
Note that particular equations (or notations or diagrams) can be captured with linked notation. The Nernst equation is (equation [for])(voltage)(of)(electrochemical cell).