What is factor e^{2x-y}dx+e^{y-2x}dy ?

The solution to factor e^{2x-y}dx+e^{y-2x}dy is e^{-y-2x}(e^{4x}dx+e^{2y}dy)

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factor e^{2x-y}dx+e^{y-2x}dy

factor

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

e^{- y - 2 x} (e^{4 x} d x + e^{2 y} d y)

Solution steps

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

Apply exponent rule:

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

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

Apply exponent rule:

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

e^{2 x} = e^{- 2 x} e^{4 x}, e^{y} = e^{- y} e^{2 y}

= e^{- 2 x} e^{4 x} e^{- y} d x + e^{- y} e^{2 y} e^{- 2 x} d y

Factor out common term

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

= e^{- y} e^{- 2 x} (e^{4 x} d x + e^{2 y} d y)

Refine

= e^{- 2 x - y} (e^{4 x} d x + e^{2 y} d y)

e^{- 2 j t - 3} + e^{2 j t - 3}

(2 a + b - c)^{2} - (a + b)

\frac{d}{d θ} ((t) (cot (θ) y (t, θ)))

- \frac{1}{5} x^{2} + 2 x - 4

What is factor e^{2x-y}dx+e^{y-2x}dy ?
The solution to factor e^{2x-y}dx+e^{y-2x}dy is e^{-y-2x}(e^{4x}dx+e^{2y}dy)