Solve the differential equation: frac{dy}{dx} | vedclass

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(C) Given the differential equation: $\frac{dy}{dx} = e^{x+y}$ Using the property of exponents,we can write: $\frac{dy}{dx} = e^x \cdot e^y$ Separatin

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$e^x + e^{-y} = c$

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(C) Given the differential equation: $\frac{dy}{dx} = e^{x+y}$ Using the property of exponents,we can write: $\frac{dy}{dx} = e^x \cdot e^y$ Separating the variables,we get: $\frac{dy}{e^y} = e^x dx$ This can be rewritten as: $e^{-y} dy = e^x dx$ Integrating both sides: $\int e^{-y} dy = \int e^x dx$ Performing the integration: $-e^{-y} = e^x + C_1$ Rearranging the terms: $e^x + e^{-y} = -C_1$ Letting $-C_1 = c$,we get the final solution: $e^x + e^{-y} = c$

Solve the differential equation: $\frac{dy}{dx} = e^{x+y}$

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