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Thanks to the contributors at Wikipedia here is the answer...
Equations can be classified according to the types of operations and quantities involved. Important types include:
- An algebraic equation is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
- A linear equation is an algebraic equation of degree one.
- A polynomial equation is an equation in which a polynomial is set equal to another polynomial.
- A transcendental equation is an equation involving a transcendental function of one of its variables.
- A functional equation is an equation in which the unknowns are functions rather than simple quantities.
- A differential equation is an equation involving derivatives.
- An integral equation is an equation involving integrals.
- A Diophantine equation is an equation where the unknowns are required to be integers.
- A quadratic equation
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