What is the answer to solvefor y,x=sqrt(y)e^y ?

The answer to solvefor y,x=sqrt(y)e^y is y=(\W(2x^2))/2

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solvefor y,x=sqrt(y)e^y

solve for

y, x = y e^{y}

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

Solution steps

x = y e^{y}

Prepare

x = y e^{y}

for Lambert form:

x^{2} = e^{2 y} y

Rewrite the equation with

2 y = u

and

y = \frac{u}{2}

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

Rewrite

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

in Lambert form:

e^{u} u = 2 x^{2}

Solve

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

u = W (2 x^{2})

Substitute back

u = 2 y,

solve for

y

Solve

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

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

Verify Solutions:

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

True

The solution is

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

Verify Solutions:

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

True

The solution is

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

2^{2 x} + 8 (2^{x}) + 7 = 0

4^{x} = 23

e^{5 x} = 6

(\frac{1}{2})^{3 x} = 8

x, 2 t = e^{x} - e^{- x}

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