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Basis of the vector space of solutions to a differential equation.

  1. Mar 5, 2009 #1
    Apologies, have solved this question.
    Answer if useful for anyone:
    Basis= {e^(5x),e^(-10x)}.

    1. The problem statement, all variables and given/known data

    Consider the differential equation
    (2nd derivative of y wrt x) + 5(1st derivative of y wrt x) - 50y =0

    Find a basis of the vector space of solutions of the above differential equation. You should separate each vector with a comma, and each should take the value of 1 at x=0

    2. Relevant equations


    3. The attempt at a solution

    Solution: y(x)=Ae^(5x) + Be^(-10x)
    The solutions are a linear combination of these two terms.
    I'm unsure of how to convert this into 'a basis of the vector space of solutions'.
    Last edited: Mar 5, 2009
  2. jcsd
  3. Mar 5, 2009 #2


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    Homework Helper

    So take values of A and B, to give particular solutions. List them.
    The value must not be the same and A+B must equal one.
    say s!=t

    you can also just chose particular s and t
    The book answer results from the choice s=1,t=0
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