Problem $2$: System linearization

Please linearize the following nonlinear systems around one of the equilibrium points. Assume

$u=1$ for both systems.

a$)$

$\left[\begin{array}{c}{x}_1^{}(t)\end{array}\right]$

$x_2^{}(t)=\left[\begin{array}{c}3x_2(t)\end{array}\right]$

$x_1(t)x_2(t)+x_1(t)+2u^2(t)$

$y(t)=3x_1{x}_2$

b$)$

$\left[\begin{array}{c}{x}_1^{}(t)\end{array}\right]$

$x_2^{}(t)=\left[\begin{array}{c}sin(x_2(t))\end{array}\right]$

$-2x_1(t)x_2(t)+x_1^2(t)-u(t)$

$y(t)=3x_1$

Problem $3$: Transfer function

a$)$ Please derive transfer function representations for the following two systems represented by

differential equations.

$y^{}(t)+8y^{}(t)=u(t)$

b$)$ Please derive transfer function representations of the linearized systems in Problem $2.$