(a)[3]
Show that $\frac{dy}{dx} = \frac{2e^{2x}y}{e^{y} - e^{2x}}$.
(b)[2]
Show that the curve has no stationary points.
(c)[4]
Show that the $x$-coordinate of $P$ satisfies the equation $x = \ln 10 - \tfrac{1}{2}\ln(2x - 1)$.
(d)[3]
Apply an iterative formula, based on the equation in part (c), to determine the $x$-coordinate of $P$ correct to $3$ significant figures. Begin with $2$ and record each iteration to $5$ significant figures.