4. The curve \(C\) has the equation \(y \mathrm { e } ^ { - 2 x } = 2 x + y ^ { 2 }\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
The point \(P\) on \(C\) has coordinates \(( 0,1 )\).
- Find the equation of the normal to \(C\) at \(P\), giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers.