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

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

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solvefor y,y=e^{xy}

solve for

y, y = e^{x y}

y = - \frac{W ( - x )}{x}

Solution steps

y = e^{x y}

Prepare

y = e^{x y}

for Lambert form:

y e^{- x y} = 1

Rewrite the equation with

- x y = u

and

y = - \frac{u}{x}

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

Rewrite

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

in Lambert form:

e^{u} u = - x

Solve

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

u = W (- x)

Substitute back

u = - x y,

solve for

y

Solve

- x y = W (- x) : y = - \frac{W ( - x )}{x}

y = - \frac{W ( - x )}{x}

1 8^{3 n} - 4 = 49

2^{5 y + 1} = 2

y, e^{x y} + ln (x) = 10

3^{x} \times 5^{2 x} = 150

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