Find the solution to the following separable differential equation. 
, a is a constant.
Definitions:
Allowance Factor
A coefficient applied to account for uncertainties, variations, or additional capacity in calculations or designs.
Standard Time
The pre-determined time allowed for the completion of a specific task, under normal working conditions.
Performance Rating
An evaluation measure used to assess the efficiency, effectiveness, or output level of employees, processes, or equipment against predefined standards.
Observed Time
The actual amount of time recorded for a task or process operation based on direct observation.
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