here is the equation:

$\frac{\partial\alpha(r,\phi)}{\partial r}=\beta\sin\alpha(r,\phi)\cos\alpha(r,\phi)$

$r$, and $\phi$ are cylindrical coordinates. $\phi$ is the angle off the x-axis. So it ranges from (0,2$\pi$). And $\beta$ is a constant.

$\alpha$ is also an angle that ranges from (0,2$\pi$)

Does anyone know how to solve this sort of an equation?

References, like a handbook of differential equations or something would be appreciated as well.

I've used Mathematica and it does give a solution. But I would like to see a derivation.

Thanks, ahead.


There is no derivative with respect to $\phi$, so we treat $\phi$ as constant. Your differential equation is separable.


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