Show me the steps to solve two bar system

$($a$)$ using large deflection theory, derive $($i$)$ the equation defining equilibrium condition,

and $($ii$)$ the equation defining the limit of stability $($employing both the stiffness criterion

and the perturbation technique$),$ assuming the rod to be rigid. Express the equations in

terms of the non$-$dimensional parameters P$/($ka$)$ and Q$/($ka$)$ and rotation $\backslash$theta of the rod.

Draw plots of P$/($ka$)$ Vs $\backslash$theta