What is the solution for yln(x)(dx}{dy}=(\frac{y+1)/x) ?

The solution for yln(x)(dx}{dy}=(\frac{y+1)/x) is y=\W((x^{(x^2)/2})/(e^{(x^2-c_{1))/4}})

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yln(x)(dx}{dy}=(\frac{y+1)/x)

y ln (x) \frac{d x}{d y} = (\frac{y + 1}{x})

y = W (\frac{x ^{\frac{x ^{2}}{2}}}{e ^{\frac{x ^{2} - c _{1}}{4}}})

Solution steps

y ln (x) \frac{d}{d y} (x) = (\frac{y + 1}{x})

Solve separable ODE:

y = W (\frac{x ^{\frac{x ^{2}}{2}}}{e ^{\frac{x ^{2} - c _{1}}{4}}})

y = W (\frac{x ^{\frac{x ^{2}}{2}}}{e ^{\frac{x ^{2} - c _{1}}{4}}})

y \cdot \frac{d y}{d x} = 5 x (y^{2} + 2)^{4}

t^{^{'}} + t = 0

3 y^{2} \frac{d y}{d x} = 5 x

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

y^{^{'}} = e^{- y} (2 x - 4), y (6) = 0

What is the solution for yln(x)(dx}{dy}=(\frac{y+1)/x) ?
The solution for yln(x)(dx}{dy}=(\frac{y+1)/x) is y=\W((x^{(x^2)/2})/(e^{(x^2-c_{1))/4}})