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Math Help - Solving a differential equation

  1. #1
    Junior Member
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    Solving a differential equation

    I have the following differential equation

    \frac{\partial}{\partial t}\left(\frac{a}{X}\right)+\frac{X}{b}\frac{\parti  al Y}{\partial t}+\frac{c}{X}=0

    where a, b and c are constants and X is a function of
    t. I want to solve it for Y analytically (if possible) or numerically.

    Note: the second term is \frac{X}{b}\frac{\partial Y}{\partial t}.
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  2. #2
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    Re: Solving a differential equation

    Hey JulieK.

    The first hint I would suggest is to multiply both sides by X. Also is Y independent of X and t?
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  3. #3
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    Re: Solving a differential equation

    Hi Chiro

    Many thanks!
    What is the advantage of multiplying both sides by X.
    Y is dependent on both X and t.

    By the way, I obtained the following relation which may help to find a solution

    Y=\frac{d}{O}\left(X^{1/2}-O^{1/2}\right)

    where d is a constant and O is a known function of t with
    a closed analytical form.
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  4. #4
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    Re: Solving a differential equation

    With regard to the hint, you might want to try differentiating your hint function and then compare this to the structure of the DE to obtain the O function.
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