The general solution of the differential equa | vedclass

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Question

(B) Given the differential equation $\frac{dy}{dx} = e^{x-y}$.Using the property of exponents, we can write $\frac{dy}{dx} = \frac{e^x}{e^y}$.By separ

Vedclass · Accepted Answer

$e^x - e^y = c$

Vedclass · Answer

(B) Given the differential equation $\frac{dy}{dx} = e^{x-y}$.Using the property of exponents, we can write $\frac{dy}{dx} = \frac{e^x}{e^y}$.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 $e^x - e^y = -C$, which can be written as $e^x - e^y = c$ (where $c = -C$ is an arbitrary constant).

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

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