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Why doesn't the integrating factor e to an integral seem to use a constant of integra

  1. Jan 31, 2010 #1
    whenever i see that integrating factor for solving a linear differential equation with
    eint. p(x) dx and then multiplied out in the equation, there seems to be no constant. i tried solving an equation with it the other day, and got an incorrect solution because of it (i think. at least i got a correct solution when i neglected it).
    why is this?
     
  2. jcsd
  3. Jan 31, 2010 #2
    Re: why doesn't the integrating factor e to an integral seem to use a constant of int

    Check this example:

    http://en.wikipedia.org/wiki/Examples_of_differential_equations

    The section "Non-separable first-order linear ordinary differential equations". An arbitrary additive term in the integral in the exponential, can be written as a constant prefactor on [tex]\mu[/tex]. Since the whole equation is multiplied by [tex]\mu[/tex], this is irrelevant for finding the solution.

    And you can se in the explicit expression for the final solution y that you have the freedom to redefine [tex]\mu[/tex] by multiplying it ba any nonzero number, since the parameter C is not determined.

    Torquil
     
  4. Jan 31, 2010 #3
    Re: why doesn't the integrating factor e to an integral seem to use a constant of int

    cool, thanks.
     
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