Find the general solution of the differential equation `(dy)/(dx)=(x+1)/(2-y),(y!=2)`

Explanation

Given differential equation is `\frac{d y}{d x}=\frac{x+1}{2-y}`
$$ \Rightarrow(2-y) y=(x+1) x $$
$$\Rightarrow \int(2-y) y=\int(x+1) x$$ (By integrating above equation)
$$\Rightarrow 2 \mathrm{y}-\frac{y^{2}}{2}=\frac{x^{2}}{2}+\mathrm{x}+\mathrm{C}$$, where `c` is an integral constant.
$$
\begin{aligned}
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