From Wikipedia

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