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Need solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.7 question 3

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Answer: \log |y|=e^{x}+x+c

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

Given: \frac{d y}{d x}=\left(e^{x}+1\right) y

Solution: \frac{d y}{d x}=\left(e^{x}+1\right) y

            \frac{d y}{y}=\left(e^{x}+1\right) d x

Integrating on both sides

            \log |y|=e^{x}+x+c

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