Find the particular solution of the differential equation `(dy)/(dx)+ycotx=2x+x^2cotx (x!=0)` given that `y = 0` when `x=pi/2`.

Explanation

To find the particular solution of the differential equation

\[ \frac{dy}{dx} + y \cot x = 2x + x^2 \cot x \quad (x \neq 0) \]

given that \( y = 0 \) when \( x = \frac{\pi}{2} \), we will follow these steps:

...