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

The solution for (e^y+6*x)*dx+(x*e^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 \cdot x) \cdot d x + (x \cdot e^{y}) \cdot d y = 0

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

Solution steps

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

Solve exact ODE:

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

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

x \to 16 lim (4 - x)

\int \frac{( x + 2 )}{x ^{2} + 4 x} d x

y = arcsin (6 x + 1)

\int \frac{2 x ^{2} + x - 8}{x ^{3} + 4 x} d x

\frac{\partial}{\partial y} (\frac{x ^{2} - y ^{2}}{z ^{2}})

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