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Provide solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.7 question 6

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Answer: e^{y}=e^{x}+c

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

Given: e^{y-x} \frac{d y}{d x}=1

Solution: e^{y-x} \frac{d y}{d x}=1

        \begin{aligned} &e^{y} \cdot e^{-x} \frac{d y}{d x}=1 \\\\ &\frac{e^{y}}{e^{x}} d y=d x \\\\ &e^{y} d y=e^{x} d x \end{aligned}

        Integrating both sides

        \begin{aligned} &\int e^{y} d y=\int e^{x} d x \\\\ &e^{y}=e^{x}+c \end{aligned}

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