What is the answer to solvefor y,x^2+xy=ln(y) ?

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

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solvefor y,x^2+xy=ln(y)

solve for

y, x^{2} + x y = ln (y)

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

Solution steps

x^{2} + x y = ln (y)

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{x^{2} + x y} = e^{l n (y)}

Simplify

e^{l n (y)} : y

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

Solve

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

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

Verify Solutions:

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

True

The solution is

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

4 x^{2} - 16 x + 20 = 0

2 x^{2} - x - 1 = x^{2} - 10 x + 21

2 x^{2} - 7 = 3 x^{2}

2 (x^{2} - 6) - 8 = 2

6 x^{2} - 8 x + 1 = x + 4

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