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Basis for the space of solutions (ODE)

  1. Feb 27, 2017 #1
    1. The problem statement, all variables and given/known data

    The equation given:

    dy/dt = 3*y

    A basis for the space of solutions is required.


    3. The attempt at a solution

    According to me it is e^(3*t) but it has turned out false. Why? I am considering the answer "The basis is the set of all functions of the form c*e^(3*t) but a different example was described as follows:
    "The vector space of solutions to a homogeneous ODE consists of infinitely many functions. To describe it compactly, we give a basis of the vector space. In this case, the basis has only 2 functions."

    Is it possible that my answer is correct and there is a bug here?
     
    Last edited by a moderator: Feb 27, 2017
  2. jcsd
  3. Feb 27, 2017 #2

    Math_QED

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    What is their basis? What is the vector space you are working in? Those are essential things to know.

    You are right to say that ##y(t) = Ae^{3t}## is the solution of this differential equation.
     
  4. Feb 27, 2017 #3

    LCKurtz

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    You are correct that the function ##e^{3t}## is a basis for the solution space. Perhaps the problem is typing it in a particular format for an online problem? Maybe they want something like ##\{e^{3t}\}##. In any case, you do understand it correctly.
     
  5. Feb 27, 2017 #4
    Many thanks. :) It is the main thing to understand it correctly. :) I will ask if this is a technical problem with a grader.
     
  6. Feb 27, 2017 #5

    LCKurtz

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    I will guess that they want the set notation, since a basis is a set of functions. In this case, a set containing a single function.
     
  7. Feb 27, 2017 #6
    I can only tick 'one', 'two' etc. I can't add the set notation. Perhaps 'none' of possibilities is the right answer. :) This is annoying.
     
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