en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

e^y=-y

Solution

e^{y} = - y

Solution

y = - W_{0} (1)

+1

Decimal Notation

y = - 0.56714 \dots

Solution steps

e^{y} = - y

Prepare

e^{y} = - y

for Lambert form:

1 = - e^{- y} y

Rewrite the equation with

- y = u

and

y = - u

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

Rewrite

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

in Lambert form:

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

Solve

- e^{u} (- u) = 1 : u = W_{0} (1)

u = W_{0} (1)

Substitute back

u = - y,

solve for

y

Solve

- y = W_{0} (1) : y = - W_{0} (1)

y = - W_{0} (1)

Popular Examples

8^{r} = 63

2^{x+1}*4^{x+3}=16

2^{x + 1} \cdot 4^{x + 3} = 16

4^{x + 1} = 8^{x}

(\frac{1}{4})^{p} = 4

3 \cdot 2^{x} = 5^{x - 2}

Frequently Asked Questions (FAQ)

What is the answer to e^y=-y ?
The answer to e^y=-y is y=-\W_{0}(1)