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:
$$\int_{\nu=0}^{v(t)} 1/f(\nu)\; dv=\int_{\tau=0}^t g(\tau)\; d\tau$$