Hi

I have two sets of differential equations

and

where are the dependent variables and are the variable coefficients

which depend on the independant parameter .

Suppose has solution space and

has solution space

My question is what is the Necessary and sufficient conditions for these

two equations to have an non-overlapping solution space (i.e. given when can we garantee that )?

Or even how I would start to investigate this?

thanks in advanced

M