Solution of the equation dy/dx=e^{x-y}(e^{x}-e^{y}) is

Correct Answer is : ey=ex−1+ce−exe^{y}=e^{x}-1+c e^{-e^{x}}ey=ex−1+ce−ex

Correct Answer is : ey=ex−1+ce−exe^{y}=e^{x}-1+c e^{-e^{x}}ey=ex−1+ce−ex

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BITSAT 2019 Slot 2 Solved Paper

Section: Mathematics

Question : 130 of 150

Marks: +1, -0

\frac{dy}{dx}=e^{x-y}(e^{x}-e^{y})

Solution:

We have,

\frac{dy}{dx}=e^{x-y}(e^{x}-e^{y})

⇒

\Rightarrow e^{y} \frac{dy}{dx}+e^{y} e^{x}=e^{2x}

Put

e^{y}=v

\therefore e^{y} \frac{dy}{dx}=\frac{dv}{dx}

\therefore \frac{dv}{dx}+v e^{x}=e^{2x}

This is linear equation

I.F

=e^{\int e^{x} dx}=e^{e^{x}}

\therefore

Required solution is

v \cdot e^{e^{x}} = \int e^{e^{x}} \cdot e^{2x} dx + C

v \cdot e^{e^{x}} = e^{e^{x}}(e^{x}-1)+C

\Rightarrow e^{y} \cdot e^{e^{x}} = e^{e^{x}}(e^{x}-1)+C

\Rightarrow e^{y} = e^{x}-1+c e^{-e^{x}}

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