I am given the following system.

\begin{split}
\overset{.}{x}&= y\\
\overset{.}{y}&= k(1-y^2)^{3/2}e^{-x}
\end{split}

writing $dx= \overset{.}{x}dt$ and $dy= \overset{.}{y}dt$ we arrive at 

$$\frac{ydy}{(1-y^2)^{3/2}}= ke^{-x}dx$$

Integrating both sides yields

$$(1-y^2)^{-1/2}= ke^{-x}+c.$$

How do I get close forms of $x(t)$ and $y(t)$ in terme of $t$?