A curve has equation $$\[ y^{2}=y \mathrm{e}^{-2 x}-3 x \]$$ (a) Show that $$\[ \frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{2 y \mathrm{e}^{-2 x}+3}{\mathrm{e}^{-2 x}-2 y} \]$$ (4) The curve crosses the $$\(y\)$$-axis at the origin and at the point $$\(P\)$$. The tangent to the curve at the origin and the tangent to the curve at $$\(P\)$$ meet at the point $$\(R\)$$. (b) Find the coordinates of $$\(R\)$$. (5)

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