Hi can you help me with this problem i dont know where do I start solving this one. Thanks
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That pic is sideways for me, but I will try my best.
I would write in standard linear form as:
$\displaystyle \frac{dr}{d\theta}+2\cot(\theta)r=-\csc(\theta)$
Next, we compute the integrating factor:
$\displaystyle \mu(\theta)=\exp\left(2\int \cot(\theta)\,d\theta\right)=\sin^2(\theta)$
And the ODE becomes:
$\displaystyle \sin^2(\theta)\frac{dr}{d\theta}+2\sin(\theta)\cos (\theta)r=-\sin(\theta)$
Or:
$\displaystyle \frac{d}{d\theta}\left(\sin^2(\theta)r\right)=-\sin(\theta)$
Can you proceed?