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Math Help - Integration Problem

  1. #1
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    Integration Problem

    I was doing a physics exercise and came across this:

    -14,3*dv/v = dt => integrating => 14,3*ln(vo/v) = t


    could anyone tell me how this was done?

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  2. #2
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    Re: Integration Problem

    Quote Originally Posted by infected36 View Post
    I was doing a physics exercise and came across this:

    -14,3*dv/v = dt => integrating => 14,3*ln(vo/v) = t


    could anyone tell me how this was done?

    This uses the solution of ordinary differential equations by seperation of variables of an ODE of the form:$\frac{dv}{dt}=f(v)g(t)$. It is usually written in the form:
    $$\int_{\nu=0}^{v(t)} 1/f(\nu)\; dv=\int_{\tau=0}^t g(\tau)\; d\tau$$
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