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!

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- Dec 6th 2007, 06:11 PMpaolopiaceDiff equation: arctan
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! - Dec 6th 2007, 06:49 PMtopsquark
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 - Dec 6th 2007, 08:08 PMpaolopiaceThanks topsquark - you gave me the hint...
Here is how I did:

y = tan(arctan(x) + K) = [x + tan(K)]/[1-x*tan(K)] = (x + C)/(1-x*C)

That's exactly what I was looking for! - Dec 7th 2007, 06:33 AMtopsquark