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Problem manipulating solution of a differential equation!

  1. May 1, 2012 #1
    1. The problem statement, all variables and given/known data

    [itex]Y'(u) = A(u)Y(u)[/itex]

    [itex]V(u)[/itex] is the general solution

    The question asks to show that if [itex]A(u)[/itex] is antisymetric for all [itex]u[/itex]
    i.e. [itex]^{t}A(u) = -A(u)[/itex] for all [itex]u[/itex]
    Then [itex]^{t}V(u).V(u) = I[/itex]

    2. Relevant equations

    A hint says to use the fact that [itex]V(0) = I[/itex]

    3. The attempt at a solution

    Using the fact given in the hint I have a solution

    (differentiate [itex]^{t}V(u).V(u)[/itex] and show that this is zero, therefore [itex]^{t}V(u).V(u)[/itex] is constant, and since the hint implies [itex]^{t}V(0).V(0) = I[/itex] the problem is solved)

    HOWEVER, I do not understand why [itex]V(0) = I[/itex]!
    Maybe it's something obvious which I just cannot spot!
    Please could somebody explain this to me
     
  2. jcsd
  3. May 2, 2012 #2
    V(0)=I because [itex]V(x) = K_1e^{\int A(x)\text{d}x}[/itex]
    i.e. every exp function with argument 0 is 1.
    So you have to prove that it is the solution V(x) maybe?
     
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