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Variable Separable Method

Solve: dy/d...

Question

Solve: $(d y / d x) = e^{x - y} (e^{x} - e^{y})$ .

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Solution

Given,

$\frac{d y}{d x} = e^{x - y} (e^{x} - e^{y})$

$\frac{d y}{d x} = e^{2 x - y} - e^{x - 2 y}$

integrating on both sides, we get,

$\int \frac{d y}{d x} = \int (e^{2 x - y} - e^{x - 2 y})$

$y = \frac{1}{2} e^{2 x - y} - e^{x - 2 y}$

$2 y = e^{2 x - y} - 2 e^{x - 2 y}$

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Similar questions

Q. Solve the differential equation:

\frac{d y}{d x} = e^{x - y} (e^{x} - e^{y}) .

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

Q. The general solution of

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

Q. The solution of the differential equation

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

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

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