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Math Help - Please help! ODE question

  1. #1
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    Please help! ODE question

    Hi, i need to know how to solve this ODE. Please see the attachment. The solution is 2logx but i don't know to get it. Any help would be much appreciated. thanks
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  2. #2
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    Quote Originally Posted by mbbx5va2 View Post
    Hi, i need to know how to solve this ODE. Please see the attachment. The solution is 2logx but i don't know to get it. Any help would be much appreciated. thanks
    Let  u = \frac{dF}{dx} . This should reduce it to a 1st order ODE of the form:

     \frac{1}{2}x^2 \frac{du}{dx} +xu =1

    Which can be written:


     \frac{du}{dx} +\frac{2}{x}u =\frac{2}{x^2}

    You can solve this for  u using an integrating factor! Giving a solution of the form:

     u = f(x) + C

    Then remember that:

     F = \int u dx

    Also, can I ask why you used  \partial instead of d if it's an ODE?  \partial is reserved for PDEs, or Partial Differential Equations... ie... Differential Equations of functions of more than 1 variable.
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  3. #3
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    Talking

    Sorry yes your right about the notation - i made a mistake. Thanks for the help i've managed to solve it.
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