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Homework Help: General Solution / Differential Equation

  1. Feb 17, 2014 #1
    1. The problem statement, all variables and given/known data
    Find the general solution x(t) to the following differential equation:

    dx/dt = 2t/5x

    2. Relevant equations

    dx/dt = 2t/5x

    3. The attempt at a solution
    My solution is:

    ∫5xdx = ∫2tdt
    (5/2)x^2 = t^2 + C
    x^2 = (2/5)(t^2 + C)
    x = +-√[(2/5)(t^2 + C)]

    However, when I put the problem in Mathematica, I get:

    x = +-√(2/5)√(x^2 + 5C)

    I don't see why it gets 5C as opposed to simply C?
    Last edited: Feb 17, 2014
  2. jcsd
  3. Feb 17, 2014 #2


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    No reason. C is an arbitrary constant and 5C is also an arbitrary constant. There's really no difference. Both are correct.
  4. Feb 17, 2014 #3
    I understood it to mean 5 * C . . . is that not correct?
  5. Feb 17, 2014 #4


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    Five times an arbitrary constant is an arbitrary constant.
  6. Feb 17, 2014 #5


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    Substitute your solution into the original ODE and see if it satisfies that equation. Do likewise with Mathematica's result.
  7. Feb 17, 2014 #6
    Hehe, fair enough.

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