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Popular >

2=y+2e^y

Solution

2 = y + 2 e^{y}

Solution

y = 0

Solution steps

2 = y + 2 e^{y}

Prepare

2 = y + 2 e^{y}

for Lambert form:

2 = (2 - y) e^{- y}

Rewrite the equation with

- y + 2 = u

and

y = - u + 2

2 = (2 - (- u + 2)) e^{- (- u + 2)}

Simplify

2 = e^{u - 2} u

Rewrite

2 = e^{u - 2} u

in Lambert form:

e^{u} u = 2 e^{2}

Solve

e^{u} u = 2 e^{2} : u = 2

u = 2

Substitute back

u = - y + 2,

solve for

y

Solve

- y + 2 = 2 : y = 0

y = 0

Popular Examples

7^{3x}=7^{12sqrt(5)}

7^{3 x} = 7^{125}

3^{x - 20} = 27

16^{3x}=8^{x+2}

1 6^{3 x} = 8^{x + 2}

e^{x^{2}} = e^{81}

(5)^{x} = 17

Frequently Asked Questions (FAQ)

What is the answer to 2=y+2e^y ?
The answer to 2=y+2e^y is y=0