What is the answer to solvefor x,xye^{y/x}=5 ?

The answer to solvefor x,xye^{y/x}=5 is x=-y/(\W(-\frac{y^2){5})}

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solvefor x,xye^{y/x}=5

solve for

x, x y e^{\frac{y}{x}} = 5

x = - \frac{y}{W ( - \frac{y ^{2}}{5} )}

Solution steps

x y e^{\frac{y}{x}} = 5

Rewrite the equation with

- \frac{y}{x} = u

and

x = - \frac{y}{u}

(- \frac{y}{u}) y e^{- u} = 5

Rewrite

(- \frac{y}{u}) y e^{- u} = 5

in Lambert form:

e^{u} u = - \frac{y ^{2}}{5}

Solve

e^{u} u = - \frac{y ^{2}}{5} : u = W (- \frac{y ^{2}}{5})

u = W (- \frac{y ^{2}}{5})

Substitute back

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

solve for

x

Solve

- \frac{y}{x} = W (- \frac{y ^{2}}{5}) : x = - \frac{y}{W ( - \frac{y ^{2}}{5} )}

x = - \frac{y}{W ( - \frac{y ^{2}}{5} )}

9^{3 x} = 2 7^{x + 2}

5^{- x} = 3. 5^{3 x}

3^{2 x - x^{2}} = 5^{4 x^{2} - 3 x}

8^{x} = 3

e^{- x} = 0.1

What is the answer to solvefor x,xye^{y/x}=5 ?
The answer to solvefor x,xye^{y/x}=5 is x=-y/(\W(-\frac{y^2){5})}