What is the answer to solvefor x,z=xe^{-xy} ?

The answer to solvefor x,z=xe^{-xy} is x=-(\W(-zy))/y

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solvefor x,z=xe^{-xy}

solve for

x, z = x e^{- x y}

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

Solution steps

z = x e^{- x y}

Rewrite the equation with

- x y = u

and

x = - \frac{u}{y}

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

Rewrite

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

in Lambert form:

e^{u} u = - zy

Solve

e^{u} u = - zy : u = W (- zy)

u = W (- zy)

Substitute back

u = - x y,

solve for

x

Solve

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

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

x = 0.9894 + 7^{x - 1}

2^{x + 2} - (6) (2)^{x - 1} - 8 = 0

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

e^{x} = 0.4

e^{l n (3 x)} = 11

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