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| The solution of the differential equation \(\frac{dy}{dx}=e^{y+x}+e^{y-x}\) is |
\(e^{-y}=e^{x}+e^{-x}+c\) \(e^{-y}=e^{x}-e^{-x}+c\) \(e^{-y}=e^{-x}-e^{x}+c\) None of the above |
| \(e^{-y}=e^{-x}-e^{x}+c\) |
| \(\begin{aligned}\text{Given, }\frac{dy}{dx}&=e^{y}(e^{x}+e^{-x})\\ e^{-y}dy&=(e^{x}+e^{-x})dx\\ e^{-y}&=e^{-x}-e^{x}+c\end{aligned}\) |
