First order differential equations (integrating factor)
8
The variables \(x\) and \(y\) satisfy the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 4 + 9 y ^ { 2 } } { \mathrm { e } ^ { 2 x + 1 } } .$$
It is given that \(y = 0\) when \(x = 1\).
Solve the differential equation, obtaining an expression for \(y\) in terms of \(x\).
State what happens to the value of \(y\) as \(x\) tends to infinity. Give your answer in an exact form.