What is the answer to solvefor x,y=(x+F)e^{-x} ?

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

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solvefor x,y=(x+F)e^{-x}

solve for

x, y = (x + F) e^{- x}

x = - W (- \frac{y}{e ^{F}}) - F

Solution steps

y = (x + F) e^{- x}

Rewrite the equation with

- x - F = u

and

x = - u - F

y = (- u - F + F) e^{- (- u - F)}

Simplify

y = - e^{u + F} u

Rewrite

y = - e^{u + F} u

in Lambert form:

e^{u} u = - \frac{y}{e ^{F}}

Solve

e^{u} u = - \frac{y}{e ^{F}} : u = W (- \frac{y}{e ^{F}})

u = W (- \frac{y}{e ^{F}})

Substitute back

u = - x - F,

solve for

x

Solve

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

x = - W (- \frac{y}{e ^{F}}) - F

3.4 e^{2 - 2 n} - 9 = - 4

8 1^{5 x - 2} = 1

27 \cdot 27 = 9^{x}

10 \cdot 1 0^{\frac{x}{3}} = 1

3^{2 - x} = 27

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