Solve the following differential equation: `(x-1)(dy)/(dx)=2x y`

Explanation

Provided differential equation is
$$ \begin{aligned} &(\mathrm{x}+1)(\mathrm{dy} / \mathrm{dx})=2 \mathrm{xy} \\ &\Rightarrow \frac{d y}{y}=\left(\frac{2 x}{x+1}\right) d x \\ &\Rightarrow \frac{d y}{y}=2\left(1-\frac{1}{x+1}\right) d x \end{aligned} $$
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