Question $1.$

Consider the following non$-$linear ordinary differential equation

$(ODE),$ with the initial condition, $y(0)=1\mathrm{.}5.$

$\frac{dy(t)}{dt}=-0\mathrm{.}4y(t{)}^{2\mathrm{.}5}+\sqrt[\phantom{2}]{u(t)}$

Linearise the ODE and, by taking Laplace transforms, define

the transfer function relating the output to the input.