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Thread: To find a solution to this Differential Equation?

  1. #1
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    To find a solution to this Differential Equation?

    For the equation:

    $\displaystyle dv/dt=-kx^{1/2}$

    I do not seem to be able to solve this one to find the general solution! :S
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  2. #2
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    Are you sure that is the equation?

    could it be $\displaystyle \frac{dv}{dt}=-kt^{1/2}$

    or

    $\displaystyle \frac{dv}{dt}=-kv^{1/2}$ ?
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  3. #3
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    Quote Originally Posted by pickslides View Post
    Are you sure that is the equation?

    could it be $\displaystyle \frac{dv}{dt}=-kt^{1/2}$

    or

    $\displaystyle \frac{dv}{dt}=-kv^{1/2}$ ?

    YES sorry my bad! It is the second one! Can you help?
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  4. #4
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    Happy to kick it off for you

    $\displaystyle \frac{dv}{dt}=-kv^{1/2}$

    separating the variables you get

    $\displaystyle \frac{dv}{v^{1/2}}=-k~dt$

    Now integrate both sides

    Hint: $\displaystyle \int \frac{dv}{v^{1/2}} = 2v^{1/2}$
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  5. #5
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    Quote Originally Posted by pickslides View Post
    Happy to kick it off for you

    $\displaystyle \frac{dv}{dt}=-kv^{1/2}$

    separating the variables you get

    $\displaystyle \frac{dv}{v^{1/2}}=-k~dt$

    Now integrate both sides

    Hint: $\displaystyle \int \frac{dv}{v^{1/2}} = 2v^{1/2}$
    Right, so therefore the general solution is:

    $\displaystyle v=4(-kt+c)^{1/2}$


    am i right?
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  6. #6
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    How did you get that?

    I get $\displaystyle v = \left( \frac{-kt+C}{2}\right)^2$
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