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Need solution for  RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 47 textbook solution.

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Answer :  (a) e^{x}+e^{-y}=C

Hint : Use variable separable form i.e. take the x terms in one side and y terms to the other.

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

Explanation : \frac{d y}{d x}=e^{x} e^{y}

\begin{aligned} &\Rightarrow \frac{d y}{e^{y}}=e^{x} d x \\ \\&\Rightarrow e^{-y} d y=e^{x} d x \\ \\&\Rightarrow C-e^{-y}=e^{x} \\ \\&\Rightarrow C=e^{x}+e^{-y} \end{aligned}

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