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Find Differential Equation with This Solution

  1. Sep 17, 2013 #1
    1. Find a differential equation with the solution y(x) = (x + C)3

    The answer cannot contain C)



    2. There are no relevant equations.


    3. I'm not entirely sure how to do this; I understand that a differential equation has multiple solutions, but for some reason I'm lost on how to find the equation from the solution itself.
     
    Last edited: Sep 17, 2013
  2. jcsd
  3. Sep 17, 2013 #2

    Dick

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    Differentiate the solution. See if you can find a way to express x+C in terms of y(x).
     
  4. Sep 17, 2013 #3
    Thanks for helping me. I was working on it and I reached [itex]\frac{dy}{dx} = 3\times y^{2/3}[/itex]. I found the derivative and basically just substituted.
     
  5. Sep 17, 2013 #4

    Dick

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    And that is exactly correct. If you solve that by separation of variables, you'll get y=(x+C)^3, yes? It's worth a quick check.
     
  6. Sep 17, 2013 #5
    Yes, I do. Awesome. Hey, if you don't mind, could you just briefly look over the next question? It's the same format, but y(x) = [itex]Cx^3[/itex] and I concluded [itex] \frac{dy}{dx} = \frac{3\times y}{x} [/itex]. I just want to make sure that one is correct because the next few questions rely on it.

    Thanks again.
     
  7. Sep 17, 2013 #6

    Dick

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    You're welcome. Yes, that's a correct form. Check it the same way as the last one. Separate variables and solve it.
     
  8. Sep 17, 2013 #7
    OK, I will. Thank you very much for your help, glad to know I'm finally getting this.
     
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