The solution of dy-dx-ex-y is-

The correct option is A e^x e^y=c dydx=e^xe^y ⇒∫ e^ydy=∫ e^xdx+c_1 e^y=e^x+c_1 e^y e^x=c_1 e^y=e^x+c_1 c=e^x e^y ...

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Byju's Answer

Standard XII

Mathematics

Composite Function

The solution ...

Question

The solution of $\frac{d y}{d x} = e^{x - y}$ is:

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

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

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

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

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Solution

The correct option is A $e^{x} - e^{y} = c$
$\frac{d y}{d x} = \frac{e^{x}}{e^{y}}$
$\Rightarrow \int e^{y} d y = \int e^{x} d x + c_{1}$
$e^{y} = e^{x} + c_{1}$
$e^{y} - e^{x} = c_{1}$
$e^{y} = e^{x} + c_{1}$
$c = e^{x} - e^{y}$

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Similar questions

The general solution of the differential equation $\frac{d y}{d x} = e^{x + y}$ is
(a) $e^{x} + e^{- y} = C$
(b) $e^{x} + e^{y} = C$
(c) $e^{- x} + e^{y} = C$
(d) $e^{- x} + e^{- y} = C$

Q. The general solution of the differential equation

\frac{d y}{d x} = 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

The solution of the equation $\frac{d y}{d x} - e^{x - y} + x^{2} e^{- y}$ is
[MP PET 2004]

Q. If

e^{x} + e^{y} = e^{x + y}

, show that

\frac{d y}{d x} = - e^{y - x}

Q. If

e^{x} + e^{y} = e^{x + y}

, prove that

\frac{d y}{d x} + e^{y - x} = 0

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The solution of dydx=ex−y is:

The correct option is A ex−ey=cdydx=exey⇒∫eydy=∫exdx+c1ey=ex+c1ey−ex=c1ey=ex+c1c=ex−ey

The solution of $\frac{d y}{d x} = e^{x - y}$ is:

The correct option is A $e^{x} - e^{y} = c$
$\frac{d y}{d x} = \frac{e^{x}}{e^{y}}$
$\Rightarrow \int e^{y} d y = \int e^{x} d x + c_{1}$
$e^{y} = e^{x} + c_{1}$
$e^{y} - e^{x} = c_{1}$
$e^{y} = e^{x} + c_{1}$
$c = e^{x} - e^{y}$