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General solution to partial differential equation (PDE)

  1. Apr 11, 2012 #1
    Hi,
    I have the following PDE


    [itex]-S\frac{\partial\vartheta}{\partial\tau}+\frac{1}{2}\sigma^2\frac{X^2}{S}\frac{\partial^2\vartheta}{\partial\xi^{2}} + [\frac{S}{T} + (r-D)X]\frac{\partial\vartheta}{\partial\xi}[/itex]


    I am asked to seek a solution of the form [itex]\vartheta=\alpha_1(\tau)\xi + \alpha_0(\tau)[/itex] and give a general solution for [itex]\alpha_1(\tau)[/itex] and [itex]\alpha_0(\tau)[/itex]

    where we have
    [itex]\tau=T-t[/itex]
    and
    [itex]\xi=\frac{t}{T}-\frac{X}{S}[/itex]

    I have tried doing the partial differentials of [itex]\vartheta[/itex] with respect to τ and ε, but the answer doesnt allow me to get a general solution for the two unknown functions of τ.
    If anyone could help i would be really grateful.
    Thanks

    NOTE: the word 'partial' in the equation should be a symbol for the partial derivative.
     
    Last edited: Apr 11, 2012
  2. jcsd
  3. Apr 12, 2012 #2
    Hi !

    Sorry to say, but the wording of the problem seems very fishy (see attachment)
     

    Attached Files:

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