An arbitrary signal $v(t)$ pass through the following system,
$w'(t) + 5 w(t) = v'''(t) + 320v''(t) + 40 v' (t) + 40v(t)$
How to determine the coefficients of the following differential equation, where the input signal is $w(t)$ and the output signal is $z(t)$, So that the output $z(t) = v(t)$ (after long time when there is no transient exist any longer)?
$z'''(t) + d_2 z''(t) + d_1 z'(t) + d_0 z(t) = e_3 w'''(t) + e_2 w''(t) + e_1 w'(t) + e_0 w(t)$