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Second order DE

  1. Oct 10, 2011 #1


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    1. The problem statement, all variables and given/known data
    I must solve [itex](1-x)y''+xy'-y=(1-x)^2[/itex] knowing that y=x is a solution if the right hand side is 0. I must use this fact in order to obtain the general solution to the DE

    2. Relevant equations
    Variation of parameters?

    3. The attempt at a solution
    I'm looking at http://tutorial.math.lamar.edu/Classes/DE/VariationofParameters.aspx and I think I need to use the Variation of parameters to solve the problem.
    But I'm given only one complementary solution, not the two I would need. I really don't know how to proceed then...
    What I did was rewrite the DE into [itex]y''+y' \left ( \frac{x}{1-x} \right )-y \left ( \frac{1}{1-x} \right ) =1-x[/itex].
    Any tip will be appreciated, as usual.
  2. jcsd
  3. Oct 10, 2011 #2
    Use Reduction of Order when you have only one solution. Just let y=xv and run it through the technique.
  4. Oct 10, 2011 #3


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    Thanks, this worked out well.
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