The value of k that makes the complex-valued function

𝑓(𝑧) = 𝑒−𝑘𝑥 (cos 2𝑦 − 𝑖 sin 2𝑦)

analytic, where 𝑧 = 𝑥 + 𝑖𝑦, is _________.

(Answer in integer)

Which one of the options given is the inverse Laplace transform of $\rm \frac{1}{s^3-s}$? 𝑢(𝑡) denotes the unit-step function.

The smallest perimeter that a rectangle with area of 4 square units can have is ______ units.

(Answer in integer)

Consider the second-order linear ordinary differential equation

$\rm x^2\frac{d^2y}{dx^2}+x\frac{dy}{dx}-y=0, x\ge1$

with the initial conditions 

$\rm y(x=1)=6, \left.\frac{dy}{dx}\right|_{x=1}=2$

The value of 𝑦 at 𝑥 = 2 equals ________.

(Answer in integer)