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Please solve RD Sharma class 12 chapter Differential Equations exercise 21.7 question 1 maths textbook solution

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Answer:  \log y+c=2 x+2 \log |x-1|

Hint:Separate the terms of x and y and then integrate them.

Given:   (x-1) \frac{d y}{d x}=2 x y


        \begin{aligned} &(x-1) \frac{d y}{d x}=2 x y \\\\ &\frac{d y}{y}=\left(\frac{2 x}{x-1}\right) d x \\\\ &\frac{d y}{y}=2\left(1+\frac{1}{x-1}\right) d x \end{aligned}

        Integrating both sides

        \log y+c=2 x+2 \log |x-1|


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