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2nd Order D.E. help

  1. May 7, 2006 #1
    I'm have a lot of trouble trying to find the general solution to the following D.E.

    y'' + 6.4y' + 10.24y = e^(-3.2x)

    I get the homogeneous solution as

    C1*e^(-3.2x)+C2*x*e^(-3.2x)

    and the particular solution as 0

    So a general solution of

    Y=C1*e^(-3.2x)+C2*x*e^(-3.2x)

    I know my solution is not right, there is some trick to it, any help?

    Gab
     
    Last edited: May 7, 2006
  2. jcsd
  3. May 7, 2006 #2

    arildno

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    Dearly Missed

    You DO mean the diff.eq y''+6.4y'+10.24y=e^(-3.2x), right?
     
  4. May 7, 2006 #3
    Ops, yes I do.
     
  5. May 7, 2006 #4

    dav2008

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    The reason you obtained 0 as your particular solution in your approach is because the inhomogeneous term is also a solution to the homogeneous equation.

    What should you do in that situation?
     
  6. May 7, 2006 #5
    uh? Variation of parameters to get something like

    Yg=u1y1+u2y2+c1(x)y1+c2(x)y2

    where Yh= u1y1+u2y2

    and Yp=c1(x)y1+c2(x)y2

    ?
     
  7. May 7, 2006 #6
    So...

    Yg= u1*e^(-3.2x)+u2*x*e^(-3.2x)+0.5*(X^2)*e^(-3.2x)

    ?
     
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