Linearising a system of ODE's

Question

So I have this ODE: $$x''=\frac{-27}{13}x'+\frac{35}{13x}-\frac{4843}{283}$$ The question asks me to write a MATLAB script to linearise this ODE around any specified x value, as far as I know only first order ODE's can be linearised. So my first step was to break down this ODE into a system of first order ODE's: $$x_1'=x_2$$ $$x_2'=\frac{-27}{13}x_2+\frac{35}{13x_1}-\frac{4843}{283}$$ The problem is now I have no idea how to linearise this even on paper, the method I would have used is: ()=()+′()(−), however of course this doesn't work in this case. I'm not sure what the question is even asking really, is it to find an expression which looks like this? $$x''=mx+c\quad\text{or}\quad x'=mx+c$$ Even if you don't know MATLAB I am not sure how to approach this question even on paper so any help would be appreciated, also numerical approaches (like forcing the answer through bisection, estimate and check, is a viable way to solve this question) :)