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  • The general solution of the differential equation dy/dx = e^(x + y) is

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

            (A)    e^x + e^{-y} = C

            (B)    e^{x }+ e^{y} = C​​​​​​

            (C)    e^{-x }+ e^{y} = C

            (D)    e^{-x }+ e^{-y} = C

Answers (1)

best_answer

Given,

\frac{dy}{dx} = e^{x+y}

\\ \implies\frac{dy}{dx} = e^x.e^y \\ \implies\int \frac{dy}{e^y} = \int e^x.dx \\ \implies -e^{-y} = e^x + C \\ \implies e^x + e^{-y} = K\ \ \ \ (Option A)

Posted by

HARSH KANKARIA

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