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Math Help - Solutions to differential equations.

  1. #1
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    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?

    thanks in advanced

    M
    Last edited by mtak0114; January 29th 2010 at 03:25 AM.
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