Linear differential equation
differential equations that are linear with respect to the unknown function and its derivatives
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.