I am having trouble solving the differential equation:
$\dfrac{dy}{d{\theta}} = \dfrac{\theta \sec\left(\dfrac{y}{\theta}\right) + y}{\theta}$
I realise I need to put it in the form $\dfrac{dy}{d\theta} + h(\theta)y = 0$ and then find the integrating factor, but I'm having trouble rearranging it. I don't think it will be too hard to solve after that!
My first attempt was to divide by $\theta$ giving $\dfrac{dy}{d\theta} = \sec\left(\dfrac{y}{\theta}\right) + \dfrac{y}{\theta}$
Then I tried taking $\sec^{-1}$ giving
$\sec^{-1}\left(\dfrac{dy}{d\theta}\right) = \dfrac{y}{\theta} + \sec^{-1}\left(\dfrac{y}{\theta}\right) $
To no avail.
Any help in rearranging this will be much appreciated!