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Formatting Question

  1. Nov 2, 2007 #1
    I was doing a few homework questions and I came about a few ODEs of this form.
    For example,

    (XD^3 + 4D^2)y = 8e^x

    Im not sure what the D stands for, is it a constant, is it a derivative of y (ie. y'''), etc. ??

    In the same section of problems there were questions that I solved using undetermined coefficient method by finding both the homogenous and particular solutions.

    Any help would be appreicated.
  2. jcsd
  3. Nov 2, 2007 #2


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    Staff Emeritus
    Science Advisor

    "D" represents the differential operator. D^2 is the second derivative and D^3 is the third derivative. Is the X in "XD^3" supposed to be x?

    If you let u= D^2 y (i.e. u= y") then that equation reduces to the linear first order equation xu'+ 4y= 8e^x. You can solve that by finding the integrating factor and then integrate twice more to find y.
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