The general solution of the differential equa | vedclass

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Question

(B) The given differential equation is $\frac{dy}{dx} = e^{x+y} = e^x \cdot e^y$.By separating the variables, we get $e^{-y} \, dy = e^x \, dx$.Integr

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) The given differential equation is $\frac{dy}{dx} = e^{x+y} = e^x \cdot e^y$.By separating the variables, we get $e^{-y} \, dy = e^x \, dx$.Integrating both sides, we have $\int e^{-y} \, dy = \int e^x \, dx$.This results in $-e^{-y} = e^x + C'$, where $C'$ is the constant of integration.Rearranging the terms, we get $e^x + e^{-y} = -C'$.Letting $C = -C'$, the general solution is $e^x + e^{-y} = C$.

The general solution of the differential equation $\frac{dy}{dx} = e^{x+y}$ is . . . . . . .

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