# Thread: Solutions to differential equations.

1. ## Solutions to differential equations.

Hi

I have two sets of differential equations

$\Delta_I(x_i, C_I(\lambda))=0$ and $\Delta_{II}(x_i, C_{II}(\lambda))=0$

where $x_i$ are the dependent variables and $C$ are the variable coefficients
which depend on the independant parameter $\lambda$.

Suppose $\Delta_I$ has solution space $X_I$ and
$\Delta_{II}$ has solution space $X_{II}$

My question is what is the Necessary and sufficient conditions for these
two equations to have an non-overlapping solution space (i.e. given $x_i \in X_{I}$ when can we garantee that $x_i \not \in X_{II}~ \forall~ i$)?
Or even how I would start to investigate this?