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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

solvefor y,e^{xy}=y

solve for

y, e^{x y} = y

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

Solution steps

e^{x y} = y

Prepare

e^{x y} = y

for Lambert form:

1 = y e^{- x y}

Rewrite the equation with

- x y = u

and

y = - \frac{u}{x}

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

Rewrite

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

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}

7^{2 x + 1} = 3^{x + 3}

9^{x} \cdot 3^{x^{2}} = 8 1^{2}

e^{- x} - 9 e^{- 3 x} = 0

5^{x} = 2 5^{x - 2}

1 0^{x} = 3.94

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