Integral for an inverse with no closed-form solution I have a function that gives $t$ in terms of $y$ that has no closed-form solution for $y$ (W|A).  
I have that $$\frac{dy}{dt} = \sqrt{a - \frac{b}{y(t)}}.$$  Is there some way to set up an integral that I can evaluate that would output $y$ given $t$?
Integrating $dt$:
$$y = \int {\sqrt{a-\frac{b}{y(t)}}} dt$$
Is there anywhere I can go from here?

You'd better do the next:
$\frac{dy}{\sqrt{a - \frac{b}{y(t)}}} = dt $ then after integrating you have solution $t(y)$
