5. A curve has equation
$$y ^ { 2 } = y \mathrm { e } ^ { - 2 x } - 3 x$$
- Show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 y \mathrm { e } ^ { - 2 x } + 3 } { \mathrm { e } ^ { - 2 x } - 2 y }$$
The curve crosses the \(y\)-axis at the origin and at the point \(P\).
The tangent to the curve at the origin and the tangent to the curve at \(P\) meet at the point \(R\). - Find the coordinates of \(R\).
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