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    So according to this differential equation

    dy
    dx
    =
    x2
    y


    - If f(x) = xsquared
    g(y) = 1/y

    why when integrating does

    ydy = xsquared dx?

    (ie- what happened to the 1/y?)

    Thanks
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    (Original post by Kieran578)
    So according to this differential equation

    dy
    dx
    =
    x2
    y


    - If f(x) = xsquared
    g(y) = 1/y

    why when integrating does

    ydy = xsquared dx?

    (ie- what happened to the 1/y?)

    Thanks
    You've got the equation: \displaystyle \frac{\mathrm{d}x}{\mathrm{d}y} = \frac{x^2}{y}

    Remember that, in essence, \mathrm{d}x and \mathrm{d}y are just small bits of x and y respectively. Thus, you can 'rearrange' the equation in a similar way to one you're used to:

    - multiply through by y
    - multiply through by dx

    which gives you y\ \mathrm{d}y = x^2 \mathrm{d}x :yep:

    Then you integrate that...etc. Hope that makes sense.
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    (Original post by james.h)
    You've got the equation: \displaystyle \frac{\mathrm{d}x}{\mathrm{d}y} = \frac{x^2}{y}



    - multiply through by y
    - multiply through by dx

    which gives you y\ \mathrm{d}y = x^2 \mathrm{d}x :yep:

    Then you integrate that...etc. Hope that makes sense.

    Could you quickly demonstrate the multipying through part as i cant quite get my head around it (not why you do it, but how)
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    dy/dx = x^2/y

    so multiply through by y => (ydy)/dx = (yx^2)/y

    y/y on the right hand side cancels => (ydy)/dx = x^2

    multiply through by dx => (dxydy)/dx = x^2 dx

    dx/dx on the left hand side cancels => ydy = x^2 dx
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    (Original post by Shawshank)
    dy/dx = x^2/y

    so multiply through by y => (ydy)/dx = (yx^2)/y

    y/y on the right hand side cancels => (ydy)/dx = x^2

    multiply through by dx => (dxydy)/dx = x^2 dx

    dx/dx on the left hand side cancels => ydy = x^2 dx

    Thanks
 
 
 
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