# Runge Kutta 4th order for system coupled equations-how to do? [duplicate]

I have system of coupled differential equations:

$x_0 x_0'=\dfrac{32}{(r^4-2r^2)}$

$(x_o x_1)'=a x_0'$

$(x_o x_2)'=-x_1x_1'-a (-x_1'-\dfrac{x_0'}{x_0})$

$(x_o x_3)'=-(x_1x_2)' +a( x_2'+\dfrac{x_1'}{x_0}+\dfrac{2x_1'x_0'}{x_0^2}+\dfrac{x_1 x_0'}{x_0^2})$

Where I need to find values for $x_0, x_1, x_2, x_3$.

In equations $'$ means that is derivative $\dfrac{d}{dz}$, on the other side values of $a$ and $r$ are dependent on $z$ coordinate ($a=a(z), r=r(z)$). I have values of $x$ at the outlet boundary, I think that is boundary value problem than.

It is necessary to solve this system with Runge Kutta 4th order method, I don't know where to start when I have system of equations of this type on left side?

If I know boundary value, not initial values, does it mean that I need to rotate my geometry and equations on that way where my zero coordinate will be on the boundary, not at he inlet? Is it necessary for solution of system of this type?

• Perhaps NDSolve[system, independentvars, dependentvardomain, Method -> {"ExplicitRungeKutta", "DifferenceOrder" -> 4}].... – Michael E2 Mar 27 '18 at 23:28
• People here generally like users to post code as Mathematica code instead of images or TeX, so they can copy-paste it. It makes it convenient for them and more likely you will get someone to help you. You may find this this meta Q&A helpful – Michael E2 Mar 27 '18 at 23:29
• This looks like a dupe of this one. – J. M.'s torpor Mar 28 '18 at 0:46