How to solve this master equation?

Tspirit

Homework Statement

In Gerry's book "Introductory quantum optics", Chapter 8.5 Decoherence, Page 207, there is a calculation which doesn't give the detail derivation, who can give me the calculation from (8.26) to (8.27)?

Homework Equations

The coherent state is defined by $$\hat{a}|\alpha>=\alpha|\alpha>$$.

The Attempt at a Solution

Traditionally, we can calculate the differential equation of a complex function. However, it is about an equation of operator and the order of the operators is very important. I have no idea about it.

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