What is the answer to solvefor y,y=e^{x+y} ?

The answer to solvefor y,y=e^{x+y} is y=-\W(-e^x)

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solvefor y,y=e^{x+y}

solve for

y, y = e^{x + y}

y = - W (- e^{x})

Solution steps

y = e^{x + y}

Prepare

y = e^{x + y}

for Lambert form:

y e^{- x - y} = 1

Rewrite the equation with

- y = u

and

y = - u

(- u) e^{- x - (- u)} = 1

Simplify

- e^{- x + u} u = 1

Rewrite

- e^{- x + u} u = 1

in Lambert form:

e^{u} u = - e^{x}

Solve

e^{u} u = - e^{x} : u = W (- e^{x})

u = W (- e^{x})

Substitute back

u = - y,

solve for

y

Solve

- y = W (- e^{x}) : y = - W (- e^{x})

y = - W (- e^{x})

2^{4 x + 1} \times 8^{- x + 3} = \frac{1}{16}

2^{x + 1} + 2^{x} + 2^{x - 1} = 7

e^{\frac{x}{2}} = 2 e^{2 x}

e^{x + 1} = 6^{x + 6}

e^{x^{2} + 6} = e^{5 x}

What is the answer to solvefor y,y=e^{x+y} ?
The answer to solvefor y,y=e^{x+y} is y=-\W(-e^x)