Solve for `xa n dy :sqrt(3)sinx+cosx=8y-y^2-18 ,w h e r e0lt=xlt=4pi, y in R`

Explanation

To solve the equation \( \sqrt{3} \sin x + \cos x = 8y - y^2 - 18 \) where \( 0 < x < 4\pi \) and \( y \in \mathbb{R} \), we will follow these steps:

### Step 1: Rearranging the Equation
We start with the equation:
\[ \sqrt{3} \sin x + \cos x = 8y - y^2 - 18 \]
Rearranging gives:
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