# Thread: Diff equation: arctan

1. ## Diff 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!

2. Originally Posted by paolopiace
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

3. ## Thanks 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!

4. Originally Posted by paolopiace
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!
Ah! I had never thought to use the sum of angles formula.

-Dan