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An ODE problem

  1. Sep 23, 2013 #1
    Hi all,

    I have an ODE of the form

    [itex]\frac{d^{3}\psi}{d\xi^{3}}-A\left(\psi+\xi\frac{d\psi}{d\xi}\right)=0,[/itex]

    where [itex]\psi=C_{1}U(\xi)+C_{2}V(\xi).[/itex]

    Is there any transformation or inventive manipulation I can use here to obtain an ODE for [itex]\sigma=U(\xi)+V(\xi)[/itex]? As this is the quantity I would like to solve for.

    Thanks.
     
  2. jcsd
  3. Sep 23, 2013 #2
    Hi !
    y''(x)-A(y(x)+x*y'(x))=0
    Let t=A*x²/2
    Then a first solution is easy to see :
    U=exp(t)=exp(A*x²/2)
    Let y(x)=f(x)*exp(A*x²/2) and z=x*sqrt(A/2)
    leading to an ODE which a solution is erf(z)
    V= erf(x*sqrt(A/2))*exp(A*x²/2)
     
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