What is the answer to solvefor x,e^xy+y=x-1 ?

The answer to solvefor x,e^xy+y=x-1 is x=-\W(-y/(e^{-y-1)})+y+1

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solvefor x,e^xy+y=x-1

solve for

x, e^{x} y + y = x - 1

x = - W (- \frac{y}{e ^{- y - 1}}) + y + 1

Solution steps

e^{x} y + y = x - 1

Prepare

e^{x} y + y = x - 1

for Lambert form:

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

Rewrite the equation with

- x + 1 + y = u

and

x = - u + y + 1

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

Simplify

y = - e^{u - y - 1} u

Rewrite

y = - e^{u - y - 1} u

in Lambert form:

e^{u} u = - \frac{y}{e ^{- y - 1}}

Solve

e^{u} u = - \frac{y}{e ^{- y - 1}} : u = W (- \frac{y}{e ^{- y - 1}})

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

Substitute back

u = - x + 1 + y,

solve for

x

Solve

- x + 1 + y = W (- \frac{y}{e ^{- y - 1}}) : x = - W (- \frac{y}{e ^{- y - 1}}) + y + 1

x = - W (- \frac{y}{e ^{- y - 1}}) + y + 1

4^{x} (5^{2 x}) = 10

850 (1 - e^{- 0.06 t}) = 600

5^{x} - 2 = \frac{62 3 ^{3}}{5 ^{2}}

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

2^{x} = 2000

What is the answer to solvefor x,e^xy+y=x-1 ?
The answer to solvefor x,e^xy+y=x-1 is x=-\W(-y/(e^{-y-1)})+y+1