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Thread: Express as a differential equation in terms of x, y and t

  1. #1
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    Express as a differential equation in terms of x, y and t

    Given that two quantities x and y, both vary with time t. express the following statesments as differential equations involving x, y and t.

    The rate of change of y with respect to t is inversely proportional to x.

    $\displaystyle \frac{dy}{dt}=\frac{k}{x}$

    How do I continue?
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Express as a differential equation in terms of x, y and t

    I believe you are done.
    You expressed the statement as a DE.

    You cannot solve it without more information.
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    MHF Contributor chisigma's Avatar
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    Re: Express as a differential equation in terms of x, y and t

    Quote Originally Posted by Punch View Post
    Given that two quantities x and y, both vary with time t. express the following statesments as differential equations involving x, y and t.

    The rate of change of y with respect to t is inversely proportional to x.

    $\displaystyle \frac{dy}{dt}=\frac{k}{x}$

    How do I continue?
    The DE is 'separable variables' and can be written as...

    $\displaystyle x(t)\ dy = k\ dt$ (1)

    If x(t) is known, then the solution is obtained in standard way integrating both terms of (1). If it isn't You need another DE to find x(t) and y(t)...



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