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Two Differential Equation Problems

  1. Oct 11, 2005 #1
    Please see the PDF attatchment to view the problems. Thank you for your time.
     

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  3. Oct 12, 2005 #2

    arildno

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    Dearly Missed

    For 1:
    What diff.eq does [tex]\psi(x)e^{-a_{1}\frac{x}{n}}[/tex] fulfill?
     
  4. Oct 13, 2005 #3

    saltydog

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    The first one (too late I know but anyway):

    Let's do a simple one first:

    [tex]y^{''}+a_1y^{'}+a_2y=0[/tex]

    or:

    [tex](D^2+a_1D+a_2)y=0[/tex]

    or:

    [tex]f(D)y=0[/tex]

    Now, use the exponential shift:

    [tex]e^{cx}f(D)y=f(D-c)[e^{cx}y][/tex]

    so up there, multiply by:

    [tex]e^{a_1x/2}[/tex]

    so:

    [tex]e^{a_1x/2}f(D)y=f(D-a_1/2)[e^{a_1x/2}\phi]=0[/tex]

    can you finish it?

    [tex]f(D-a_1/2)=(D-a_1/2)^2+a_1(D-a_1/2)+a_2[/tex]
     
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