What is the solution for xdx=-(ey)/(ey+6)dy ?

The solution for xdx=-(ey)/(ey+6)dy is y=-(6\W(-1/(6e^{(-ex^2+c_{1))/(12)}}))/e-6/e

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xdx=-(ey)/(ey+6)dy

x d x = - \frac{ey}{ey + 6} d y

y = - \frac{6 W ( - \frac{1}{6 e ^{\frac{- e x ^{2} + c _{1}}{12}}} )}{e} - \frac{6}{e}

Solution steps

x d x = - \frac{ey}{ey + 6} d y

Solve separable ODE:

y = - \frac{6 W ( - \frac{1}{6 e ^{\frac{- e x ^{2} + c _{1}}{12}}} )}{e} - \frac{6}{e}

y = - \frac{6 W ( - \frac{1}{6 e ^{\frac{- e x ^{2} + c _{1}}{12}}} )}{e} - \frac{6}{e}

y^{^{'}} = 18 4 x y

y^{^{'}} + (x - 10) y^{^{'}} + y = 0

\frac{d ^{2} x}{d x ^{2}} + a \cdot \frac{d y}{d x} = b \cdot y^{- 2}

\frac{d p}{d y} \cdot p = - \frac{1}{2 y ^{3}}

y^{^{'}} = e^{(2 + 3) x + (1 + 1) y}

What is the solution for xdx=-(ey)/(ey+6)dy ?
The solution for xdx=-(ey)/(ey+6)dy is y=-(6\W(-1/(6e^{(-ex^2+c_{1))/(12)}}))/e-6/e