Initial Value Problem.
A differential equation, coupled with enough initial conditions for there to be a unique solution.
Example:
y'' - 6y = exp(x) ; y'(0) = y(0) = 0
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Algebraic equations, trigenometric equations, linear equations, geometric equations, partial differential equations, differential equations, integrals to name a few.
The answer will depend on what kinds of equations: there are linear equations, polynomials of various orders, algebraic equations, trigonometric equations, exponential ones and logarithmic ones. There are single equations, systems of linear equations, systems of linear and non-linear equations. There are also differential equations which are classified by order and by degree. There are also partial differential equations.
Olusola Akinyele
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It is an equation in which one of the terms is the instantaneous rate of change in one variable, with respect to another (ordinary differential equation). Higher order differential equations could contain rates of change in the rates of change (for example, acceleration is the rate of change in the rate of change of displacement with respect to time). There are also partial differential equations in which the rates of change are given in terms of two, or more, variables.