Linear differential equation

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In mathematics, a linear differential equation is a differential equation that is stated by a linear polynomial in the unknown function and its derivatives. It is an equation of the form:

where a0(x), ..., an(x) and b(x) are random differential functions that do not need to be linear. And y′, ..., y(n) are the derivatives of an unknown function y that follow after the variable x.

This equation is an ordinary differential equation (ODE). A linear differential equation may also be a linear partial differential equation (PDE), if the unknown function depends on several variables. And the derivatives that show in the equation are partial derivatives.