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Differential equation problems

  1. Dec 2, 2005 #1
    let be the differential equation in the form...

    [tex]L[y]=a_{0}y+a_{1}y´+a_{2}y´´-f(x)=0 [/tex]

    then you could use your theory of differential equation to solve and get the solution y=y(x), my first question is if knowing the value of y1=Y(x) and y2=g(x) being y1 and y2 solutions of the differential equation, could we obtain the values of [tex]a_{0},a_{2},a_{1}[/tex] i think you could use the Wronskian W(x) and the solution to this come from setting W(x)=0 adn from this you get the values of the a,s..

    the other question is given the differential operator..

    [tex] L[G(x,s)]=\delta(x-s) [/tex] with G(x-s) known how could obtain the a,s? (this is the inverse to the Green operator theory)..

    and the last question...given the differential operator..

    [tex]L[y]=a_{0}+a_{1}D^{1}+a_{2}D^{2}=0 [/tex]

    where the functions a,s are function of x a=A(x) for every a then how could you obtain the adjoint operator?..thanks.
  2. jcsd
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