If an inequality uses the phrase at most, it will require a greater than symbol
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Let's suppose we want to solve 
with 
. Separating variables and integrating, we get
Leaving the solution in this form, the initial condition gives
This means the solution is
.
Now if we were to write
, then we would have found
so that the solution would have been
.
But these two solutions are the same, since
. So we get the same solution regardless of where we place 
, despite getting different values for .
Leaving the solution in this form, the initial condition gives
This means the solution is
Now if we were to write
so that the solution would have been
But these two solutions are the same, since