What is the answer to solvefor x,e^{x/y}=x-y ?

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

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solvefor x,e^{x/y}=x-y

solve for

x, e^{\frac{x}{y}} = x - y

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

Solution steps

e^{\frac{x}{y}} = x - y

Prepare

e^{\frac{x}{y}} = x - y

for Lambert form:

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

Rewrite the equation with

- \frac{x}{y} + 1 = u

and

x = - y u + y

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

Simplify

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

Rewrite

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

in Lambert form:

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

Solve

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

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

Substitute back

u = - \frac{x}{y} + 1,

solve for

x

Solve

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

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

2 7^{x + 1} = 9

2 ln (5 - e^{- 2 x}) = 1

27 = 3^{x}

27 = 3^{6 - 3 x}

e^{x} - 2 x e^{x} = 0

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