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Homogeneous differential equation

  1. Apr 20, 2010 #1
    1. The problem statement, all variables and given/known data


    y1(x)=x is a solution

    find the second solution, y2(x), y1 and y2 are linear independent

    2. Relevant equations


    3. The attempt at a solution

    i only know how to find it by auxiliary equation by substitute y=erx
    and also i cant use substitution y=xr

    how to do this?
    Last edited: Apr 20, 2010
  2. jcsd
  3. Apr 20, 2010 #2


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    Homework Helper
    Gold Member

    With these types of problems, where you are given one solution you usually look for a second solution of the form [itex]y_2(x)=u(x)y_1(x)[/itex]. So, try that substitution and see what you get.
  4. Apr 20, 2010 #3



    substitute and get


    like this right?

    but it seems to become more complicated is it? or should i continue?
  5. Apr 20, 2010 #4


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    Homework Helper
    Gold Member

    You'll want to double check this :wink:
  6. Apr 20, 2010 #5
    owho, yes yes, i get the answer. thank you very much.. ^^v
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