What is factor e^{y-x}dx-e^{x-y}dy ?

The solution to factor e^{y-x}dx-e^{x-y}dy is e^{-x-y}(e^{2y}dx-e^{2x}dy)

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factor e^{y-x}dx-e^{x-y}dy

factor

e^{y - x} d x - e^{x - y} d y

e^{- x - y} (e^{2 y} d x - e^{2 x} d y)

Solution steps

e^{y - x} d x - e^{x - y} d y

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

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

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

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

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

Factor out common term

e^{- x} e^{- y}

= e^{- x} e^{- y} (e^{2 y} d x - e^{2 x} d y)

Refine

= e^{- y - x} (e^{2 y} d x - e^{2 x} d y)

a \cdot ln (x) + b \cdot ln (x)

sin (180 - 2 b)

3 x^{3} - 2 x^{2} + 8 + 12

6^{2} - 2 (6) (6)

16 x^{3} + 250 x^{3}

What is factor e^{y-x}dx-e^{x-y}dy ?
The solution to factor e^{y-x}dx-e^{x-y}dy is e^{-x-y}(e^{2y}dx-e^{2x}dy)