6 The variables \(x\) and \(y\) satisfy the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = x \mathrm { e } ^ { y - x } ,$$
and \(y = 0\) when \(x = 0\).
- Solve the differential equation, obtaining an expression for \(y\) in terms of \(x\).
- Find the value of \(y\) when \(x = 1\), giving your answer in the form \(a - \ln b\), where \(a\) and \(b\) are integers.