I'm not clear yet how to write the math symbols.
Therefore I'm wirting in plain text.
The separable differential equation I'm dealing with ends up as:
arctan(y) = arctan(x) + K
How do I find the solutions from here?
Thanks!
It would probably be better to leave the equation "as is" and figure out a value of K from initial conditions. But then you simply have
$\displaystyle y = tan(tan^{-1}(x) + K)$
The possible problem I see here is that $\displaystyle tan^{-1}(x)$ is going to return a reference angle, so technically your solution will be
$\displaystyle y = tan(tan^{-1}(x) + \pi n + K)$
where n is an integer.
I suppose the source (as it were) of the differential equation will have to tell you how to handle that.
I'm not sure if this answers your question....
-Dan