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Algebraic solution - The solution of an algebraic equation, often one that seeks zeros of a polynomial, is sometimes said to admit an "algebraic solution" or a "solution in radicals" if function that expresses the solution in terms of the coefficients relies only on addition, subtraction, multiplication, division, and the extraction of roots. The most well-known example is the solution

Singular solution - A singular solution ys(x) of an ordinary differential equation is a solution that is tangent to every solution from the family of general solutions. By tangent we mean that there is a point x where ys(x) = yc(x) and y's(x) = y'c(x) where yc is any general solution.

Viscosity solution - In mathematics, the viscosity solution concept was introduced in the early 1980's by Pierre-Louis Lions and Michael Crandall as a generalization of the classical concept of what is meant by a 'solution' to a partial differential equation (PDE). It has been found that the viscosity solution is the natural solution concept to use in many applications of PDE's, including for example in optimal control (the Hamilton-Jacobi-Bellman equation).

Corner solution - A corner solution is a special solution to an agent's maximization problem in which the quantity of one of the maximized arguments is zero. Whilst a general solution will lie in the interior at the point of tangency between the objective function and the constraint, the corner solution does not exhibit this property.

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