It is not clear whether you are asking a general question or a question about the problem you have submitted.
In the case of the equation you have submitted, variables are separable and the general solution is y=Cx-1 where C is an arbitrary constant which can be determined from some initial condition if there is one. When there is an initial condition and C is determined, that is a particular solution.
The general definition of general versus particular solution may be more complicated to state since it depends a bit upon the type of DE involved.
