What is the solution for e^y+((xe^y+1)dy)/(dx)=0 ?

The solution for e^y+((xe^y+1)dy)/(dx)=0 is y=-\W(xe^{c_{1}})+c_{1}

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e^y+((xe^y+1)dy)/(dx)=0

e^{y} + \frac{( x e ^{y} + 1 ) d y}{d x} = 0

y = - W (x e^{c_{1}}) + c_{1}

Solution steps

e^{y} + \frac{( x e ^{y} + 1 ) d y}{d x} = 0

Solve exact ODE:

y = - W (x e^{c_{1}}) + c_{1}

y = - W (x e^{c_{1}}) + c_{1}

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x \to - 4 lim (\frac{2}{( x + 4 ) ^{3}})

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What is the solution for e^y+((xe^y+1)dy)/(dx)=0 ?
The solution for e^y+((xe^y+1)dy)/(dx)=0 is y=-\W(xe^{c_{1}})+c_{1}