What is the solution for (e^y+6x)dx+(xe^y)dy=0 ?

The solution for (e^y+6x)dx+(xe^y)dy=0 is y=ln((c_{1})/x-3x)

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(e^y+6x)dx+(xe^y)dy=0

(e^{y} + 6 x) d x + (x e^{y}) d y = 0

y = ln (\frac{c _{1}}{x} - 3 x)

Solution steps

(e^{y} + 6 x) d x + (x e^{y}) d y = 0

Solve exact ODE:

y = ln (\frac{c _{1}}{x} - 3 x)

y = ln (\frac{c _{1}}{x} - 3 x)

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What is the solution for (e^y+6x)dx+(xe^y)dy=0 ?
The solution for (e^y+6x)dx+(xe^y)dy=0 is y=ln((c_{1})/x-3x)