Solve an ODE system parameters

First of all, I must say that it’s (almost) my first use of the language; I usually use Matlab or Mathematica but for this special purpose I need an open source software, so I give a chance to Julia.
Here is my problem:
I have a coupled system of ODE’s which have the following form
where a,M,E,L,Q are parameters. The boundary conditions are at infinity for each of the variables (in fact, I have computed the serie at infinity for them).
Other informations: a,M,E are fixed and will never change (don’t worry about them) but I would like to be able to varry L and Q easily and continuously if possible since they are the prameters for a surface I’d like to plot afterwards.

Is there any examples of similar codes so that I can understand the syntax ?
The right hand sides are quite simple functions involving trigonometric and powers, should I create subfunctions for a cleaner code or will it slow down the procedure ?
Any other advice ? (specific arguments to the functions…)

Thank you very much !

If you’re looking for the steady states of an IVP, use a SteadyStateProblem:

Enclose those 3, and then make the other two parameters. Then use Interact.jl to turn them into sliders: