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Thread: Help with this D.E please

  1. #1
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    Help with this D.E please

    1/v dv=-ke^(s/h) ds

    Where k is a constant

    Im trying to get v as a function of s by sep. of variables and am fairly confused by the algebra. Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by msu_15 View Post
    1/v dv=-ke^(s/h) ds

    Where k is a constant

    Im trying to get v as a function of s by sep. of variables and am fairly confused by the algebra. Any help would be appreciated.
    What is h?

    If it is just another constant then your equation is ready to be integrated...

    $\displaystyle \int \frac{1}{v} dv = -k \int e^{\frac{s}{h}}ds $
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  3. #3
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    Quote Originally Posted by msu_15 View Post
    1/v dv=-ke^(s/h) ds

    Where k is a constant

    Im trying to get v as a function of s by sep. of variables and am fairly confused by the algebra. Any help would be appreciated.
    The variables are already separated in this case. My solution only works if k and h are constants too.

    Integrating : $\displaystyle \int \frac{dv}{v} = \int -ke^{(s/h)} ds$

    $\displaystyle ln|v| = -ke^{\frac{s}{h}} \times \frac{h}{s} + C$

    Can you solve it from there? I tried going further but could only get to s^s =f(v)
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  4. #4
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    h is a constant as well. my bad
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