In a paint mixing plant, two tanks supply fluids to a mixing cistern. The height, $,$ of the fluid in the

cistern is dependent upon the difference between the input mass flow rate, $,$ and the output flow rate,

$$

$.$ A nonlinear differential equation describing this dependency is given by

$$

$+$

$$

$$

$(2)=$

$$

$$

$(5)$

where $=$ cross$-$sectional area of the cistern, $=$ cross$-$sectional area of the exit pipe, $=$

acceleration due to gravity, and $=$ liquid density.

Linearize Eq$.(5)$ for the equilibrium point $(0,0).$