Differential Equations

Let y = y(x) be the solution of the differential equation dy = e^{\(\alpha\)x + y} dx; \(\alpha\) \(\in\) N. If y(log_e2) = log_e2 and y(0) = log_e\(\left( {{1 \over 2}} \right)\), then the value of \(\alpha\) is equal to _____________.