A nonlinear system has an input$-$output model given by

$\frac{dy(t)}{dt}+y(t)(1-0\mathrm{.}2(y(t){)}^2)=2u(t)$

A$.$ Obtain the equilibrium points $y_e$ of the system for constant inputs of $u(t)=u_e,$AAt to

determine the operating points $(y_e,u_e).$

B$.$ Linearize the system with respect to the operating point $(y_e,u_e)$ and determine the

transfer function of the linearized model.

C$.$ Find an operating point for which the linearized model is unstable.