What is the solution for (x^2+y)+(x+e^y)(dy)/(dx)=0 ?

The solution for (x^2+y)+(x+e^y)(dy)/(dx)=0 is y=-\W((e^{(-x^3+3c_{1})/(3x)})/x)+(3c_{1}-x^3)/(3x)

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(x^2+y)+(x+e^y)(dy)/(dx)=0

(x^{2} + y) + (x + e^{y}) \frac{d y}{d x} = 0

y = - W \frac{e ^{\frac{- x ^{3} + 3 c _{1}}{3 x}}}{x} + \frac{3 c _{1} - x ^{3}}{3 x}

Solution steps

(x^{2} + y) + (x + e^{y}) \frac{d y}{d x} = 0

Solve exact ODE:

y = - W \frac{e ^{\frac{- x ^{3} + 3 c _{1}}{3 x}}}{x} + \frac{3 c _{1} - x ^{3}}{3 x}

y = - W \frac{e ^{\frac{- x ^{3} + 3 c _{1}}{3 x}}}{x} + \frac{3 c _{1} - x ^{3}}{3 x}

\int \frac{3 y ^{2} + 1}{y ^{3} + y} d y

\int sin^{3} (x) d x

x \to - 2 lim (x (x - 1))

\frac{2000 x}{4 x + 75}

\int y + 1 d y

What is the solution for (x^2+y)+(x+e^y)(dy)/(dx)=0 ?
The solution for (x^2+y)+(x+e^y)(dy)/(dx)=0 is y=-\W((e^{(-x^3+3c_{1})/(3x)})/x)+(3c_{1}-x^3)/(3x)