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Popular >

e^y+y=1

Solution

e^{y} + y = 1

Solution

y = 0

Solution steps

e^{y} + y = 1

Prepare

e^{y} + y = 1

for Lambert form:

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

Rewrite the equation with

- y + 1 = u

and

y = - u + 1

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

Simplify

1 = e^{u - 1} u

Rewrite

1 = e^{u - 1} u

in Lambert form:

e^{u} u = e

Solve

e^{u} u = e : u = 1

u = 1

Substitute back

u = - y + 1,

solve for

y

Solve

- y + 1 = 1 : y = 0

y = 0

Popular Examples

(e^{1/x})/(x^2)=0

\frac{e ^{\frac{1}{x}}}{x ^{2}} = 0

3^{log_{81}(2x+5)}=4

3^{l o g_{81} (2 x + 5)} = 4

(1/3)^x=9^{1-2x}

(\frac{1}{3})^{x} = 9^{1 - 2 x}

(5^x)^35^{2x-1}=5

(5^{x})^{3} 5^{2 x - 1} = 5

solvefor m,1=y^{6m}solve for

m, 1 = y^{6 m}

Frequently Asked Questions (FAQ)

What is the answer to e^y+y=1 ?
The answer to e^y+y=1 is y=0