How reduce the differential equation to first order ?

For example:

$\displaystyle \frac{d^5y}{dx^5}+c_1 \frac{d^4y}{dx^4}+c_2 \frac{d^3y}{dx^3}+c_3 \frac{d^2y}{dx^2}+c_4 \frac{dy}{dx} = f(x)$

and write the resulting system of equations in the form:

$\displaystyle \vec{z} = A \vec{z} + Bf(x)$