What is the answer to solvefor y,e^{xy}=2y ?

The answer to solvefor y,e^{xy}=2y is y=-(\W(-x/2))/x

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solvefor y,e^{xy}=2y

solve for

y, e^{x y} = 2 y

y = - \frac{W ( - \frac{x}{2} )}{x}

Solution steps

e^{x y} = 2 y

Prepare

e^{x y} = 2 y

for Lambert form:

1 = 2 y e^{- x y}

Rewrite the equation with

- x y = u

and

y = - \frac{u}{x}

1 = 2 (- \frac{u}{x}) e^{u}

Rewrite

1 = 2 (- \frac{u}{x}) e^{u}

in Lambert form:

e^{u} u = - \frac{x}{2}

Solve

e^{u} u = - \frac{x}{2} : u = W (- \frac{x}{2})

u = W (- \frac{x}{2})

Substitute back

u = - x y,

solve for

y

Solve

- x y = W (- \frac{x}{2}) : y = - \frac{W ( - \frac{x}{2} )}{x}

y = - \frac{W ( - \frac{x}{2} )}{x}

4 e^{2 x} x^{2} + 8 e^{2 x} x + 2 e^{2 x} = 0

y, e^{x y} = 4 y

1000 (1.03)^{t} = 5000

3^{2 x} - 28 \times 3^{x} + 27 = 0

1808 = 60 t + 1800 e^{- \frac{t}{30}}

What is the answer to solvefor y,e^{xy}=2y ?
The answer to solvefor y,e^{xy}=2y is y=-(\W(-x/2))/x