6 The variables \(x\) and \(y\) satisfy the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 4 \frac { \mathrm {~d} y } { \mathrm {~d} x } = 12 \mathrm { e } ^ { 2 x }$$
- Find the general solution of the differential equation.
- It is given that the curve which represents a particular solution of the differential equation has gradient 6 when \(x = 0\), and approximates to \(y = \mathrm { e } ^ { 2 x }\) when \(x\) is large and positive. Find the equation of the curve.