Number of parameters for a nonlinear differential equation

[marellasunny]

Take for example a system
$\frac{dx_i}{dt}$=(x_i,t,a,b,...) i-number of state equations.
What would be the maximum number of parameters permitted for this system of non-linear differential equations?

Is it finally determined by the solution space?Is there a criteria for number of parameters in a system of differential equations?

 

[HallsofIvy]

Perhaps I am misundersanding your question. You can have any number of parameters in a differential equation.