When solving transcendental equations,
Solve frequently warns us that inverse functions are being used so that some solutions may not be found.
We also see that
Reduce might provide a more complete solution and, indeed, simply changing
Reduce provides a complete, quantified result.
Somtimes, however, this same message is produced by
My guess is that
Solve which in turn generates the message. Is it possible, though, to access
DSolve? For this particular equation, it would be easy enough to separate variables,
Integrate and then apply
Reduce. I'm wondering about a more general solution, though.