# How to solve given trigonometric equation

I've got a stream function:

$$u_\infty y + \frac{Q}{2\pi} \operatorname{arctg}\frac{y}{x} = 0$$

How do I solve it for y? I know the solution, just don't know how to get there step by step.

EDIT: The solution given in the book is: $$x = -y \operatorname{ctg} \left( \frac{2 \pi u_\infty}{Q} \right)$$

I'm sorry, I actually didn't realize the given solution is for x, not y.

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So, what's the solution that you know? – Kaster Feb 17 '13 at 10:21
@Kaster see above, edited my question – mmm Feb 17 '13 at 10:26
Actually, that's not right; there should be a $y$ in the $\cot$, see my answer below. – Ron Gordon Feb 17 '13 at 10:26
@rlgordonma yes, you're right, there's an (now) obvious error in my materials. – mmm Feb 17 '13 at 10:32

You essentially have an equation for $y$ of the form
$$x = -\frac{y}{\tan{a y}}$$
where $a=2 \pi u_{\infty}/Q$. There is no analytical solution for $y$ in terms of $x$ and $a$, but there are ways to approximate the solution depending on the domain of $x$.
what is $\mu_{\infty}$ and $Q$ mean? – yiyi Feb 17 '13 at 10:17
$u_\infty$ stands for flow velocity in the x-direction, you could skip the subscript, it's just used to indicate undisturbed flow in the materials I'm studying i.e. "long before flow reaches the obstacle". Q is spring discharge. I've never studied fluid mechanics before and don't know english nomenclature, hope I didn't confuse anything. – mmm Feb 17 '13 at 10:43