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Math Help - Can someone help with and explain this differential equation?

  1. #1
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    Exclamation Can someone help with and explain this differential equation?

    I know it looks easy, but my working does not look right!

    (x + 1) dy/dx - 2xy = 2x (x + 1)

    1) which analytical method would you use to solve this equation?
    and therefore solve expressing y explicitly as a function of x.
    Hence find the particular solution of the differential equation that satisfies the initial condition y(0) = 1

    Many thanks
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  2. #2
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    Hi. I would divide through by (x^2+1). That puts it into standard form of a first order ode. Now calculate the integrating factor and proceed.
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  3. #3
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    I am working on this similar problem - I think I have got to the last step and am trying to integrate the following...

    \int e^{x^2}2x dx

    Should be integrating this by parts?

    I have seen in another text where this has been integrated it in one go but I don't know if this is right?

    Please help!!
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  4. #4
    Super Member Aryth's Avatar
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    You can integrate this by substitution, let:

    u = x^2

    Then

    \frac{du}{dx} = 2x

    And then:

    du = 2x ~dx

    Which turns your integral into:

    \left[\int e^u ~du\right]_{u = x^2}

    Or you can recognize that:

    \frac{d}{dx} \left[e^{x^2}\right] = e^{x^2}2x

    Your integral would be:

    \int \frac{d}{dx}\left[e^{x^2}\right] ~dx

    Which is really easy as well.
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