Solving the ODE equations

can anyone help me find the way to get the solution to the equation mentioned below,

The equation will keep on going for x6, but if anyone can guide me to find the first three solution, I can replicate it

I believe this is first order differential equation.

[John D'Errico]

You cannot solve anything with only the first three equations, and 6 variables.

You MIGHT be able to simply enough use an ODE solver, like ODE45 to solve it.

Is it linear? No, because of the products in there between variables (x1*x2, etc.) it is not linear. Were it purely linear, then a matrix exponential would solve it for you simply and easily, but that is not the case here. If the constants are not known, then the solution will be non-trivial for a nonlinear problem.

Your option, IF the constants are unknown, is purely and only dsolve, and I would not be surprised if it grinds for a LONG time, if it ever terminates.

If the constants are known, and you are willing to accept a purely numerical solution, and you have initial values, are then anything from the ODE family of tools. So ODE45, ODE23s, etc.

Read the help for the specific tool, once you decide which of the cases apply as I have listed them. You willl find worked examples in there, so there is no need for someone to write the code for you.