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

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

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

(x^{2} + y) d x + (x - e^{y}) d y = 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) d x + (x - e^{y}) d y = 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}

y = 4

\frac{d}{d x} (\frac{1}{x ^{- 2}})

\frac{\partial}{\partial x} (\frac{e \cdot x}{c - x})

x \to 4 - lim (\frac{- 2}{x ^{2} - 16})

2 x^{2} - 3

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