Linear differential equation

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:

${\displaystyle a_{0}(x)y+a_{1}(x)y'+a_{2}(x)y''\cdots +a_{n}(x)y^{(n)}=b(x)}$

where a₀(x), ..., a_n(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.