What is factor e^{x+y}dx+e^{2x-3y} ?

The solution to factor e^{x+y}dx+e^{2x-3y} is e^{-3y+2x}(e^{3x}dx+1)

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factor e^{x+y}dx+e^{2x-3y}

factor

e^{x + y} d x + e^{2 x - 3 y}

e^{- 3 y + 2 x} (e^{3 x} d x + 1)

Solution steps

e^{x + y} d x + e^{2 x - 3 y}

Apply exponent rule:

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

= e^{y} e^{x} d x + e^{2 x} e^{- 3 y}

Apply exponent rule:

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

e^{y} = e^{- 3 y} e^{4 y}, e^{2 x} = e^{x} e^{x}

= e^{x} e^{- 3 y} e^{4 y} d x + e^{x} e^{x} e^{- 3 y}

Factor out common term

e^{- 3 y} e^{x}

= e^{- 3 y} e^{x} (e^{4 y} d x + e^{x})

Factor

e^{x} + e^{4 y} d x : e^{x} (e^{3 x} d x + 1)

= e^{x} e^{x} e^{- 3 y} (e^{3 x} d x + 1)

Refine

= e^{2 x - 3 y} (e^{3 x} d x + 1)

25 e^{2} - 60 e f + 36 f^{2}

cos (h) (a t)

(x + 3)^{2} - 2 (x + 3) - 8

[- x]

(- 4 x^{3} n) - 8

What is factor e^{x+y}dx+e^{2x-3y} ?
The solution to factor e^{x+y}dx+e^{2x-3y} is e^{-3y+2x}(e^{3x}dx+1)