Linear differential equation

Template:About 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:

$a_0(x)y+a_1(x)y^{\prime }+a_2(x)y^{″}\cdots +a_n(x)y^{(n)}=b(x)$

where Template:Nowrap and Template:Math are random differential functions that do not need to be linear. And Template:Math are the derivatives of an unknown function Template:Math that follow after the variable Template:Math.

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.