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Theory of linear ODEs

  1. Feb 20, 2008 #1
    Suppose I already have a solution [itex]u[/itex] to a first order ODE.

    If I try to solve this ODE without initial conditions and I get another solution [itex]w[/itex], then it can be regarded as a function of an arbitrary constant: [itex]w=w(C)[/itex].

    Is it true to say that [itex]u = w(C)[/itex] for some C? If so, how do I find such a C?
  2. jcsd
  3. Feb 20, 2008 #2


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    That's a little vague. You use the boundary conditions to find C. In general, an ODE doesn't even have a unique solution unless you make some assumptions about the form of the ODE. Can you be more concrete?
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