I have the following differential equation

$\displaystyle \frac{\partial}{\partial t}\left(\frac{a}{X}\right)+\frac{X}{b}\frac{\parti al Y}{\partial t}+\frac{c}{X}=0$

where $\displaystyle a$, $\displaystyle b$ and $\displaystyle c$ are constants and $\displaystyle X$ is a function of

$\displaystyle t$. I want to solve it for $\displaystyle Y$ analytically (if possible) or numerically.

Note: the second term is $\displaystyle \frac{X}{b}\frac{\partial Y}{\partial t}$.