7 The variables \(x\) and \(y\) satisfy the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = x \mathrm { e } ^ { x + y }$$
and it is given that \(y = 0\) when \(x = 0\).
- Solve the differential equation and obtain an expression for \(y\) in terms of \(x\).
- Explain briefly why \(x\) can only take values less than 1 .