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Math Help - Separation of Variables question!

  1. #1
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    Post Separation of Variables question!


    v (dv/dx) = - (1/250) vē - g

    solve the equation for v as a function of x

    this is for upward motion using quadratic model of air resistance
    thanks
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  2. #2
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    Quote Originally Posted by acu04385 View Post

    v (dv/dx) = - (1/250) vē - g

    solve the equation for v as a function of x

    this is for upward motion using quadratic model of air resistance
    thanks
    Is g a constant?

    If so...

    v\,\frac{dv}{dx} = -\frac{1}{250}v^2 - g

    \frac{dv}{dx} = -\frac{1}{250}v - gv^{-1}

    \frac{dv}{dx} = -\frac{v}{250} - \frac{g}{v}

    \frac{dv}{dx} = \frac{-v^2 - 250g}{250v}

    \frac{dv}{dx} = -\frac{v^2 + 250g}{250v}

    \frac{dx}{dv} = -\frac{250v}{v^2 + 250g}

    \frac{dx}{dv} = -250v(v^2 + 250g)^{-1}.

    You can now solve this with a u substitution.
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